Brownian motion

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The Concepts and Practice of Mathematical Finance by Mark S. Joshi

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Black-Scholes formula, Brownian motion, correlation coefficient, Credit Default Swap, delta neutral, discrete time, Emanuel Derman, implied volatility, incomplete markets, interest rate derivative, interest rate swap, London Interbank Offered Rate, martingale, millennium bug, quantitative trading / quantitative finance, short selling, stochastic process, stochastic volatility, the market place, time value of money, transaction costs, value at risk, volatility smile, yield curve, zero-coupon bond

The general case follows from approximating by piecewise constant functions. 8.6 The joint distribution of minimum and terminal value for a Brownian motion with drift In Section 8.4, we derived the joint law of the minimum and terminal value for a Brownian motion without drift. In this section, we combine that result with our results on Girsanov's theorem to derive the joint law for a Brownian motion with drift. Let Wt be a Brownian motion. Let Yt = aWt, and my be the minimum of Yt up to time t. We then have for y < 0 and x > y that ?(Yt > x, m ' < y) = I1(Yt < 2y - x). (8.37) This follows from the result for Brownian motion, (8.20), as the volatility term makes no real difference. We wish to prove an analogous result for a Brownian motion with drift. Let Zt = vdt + 6dWt (8.38) and mZ denotes its minimum up to time t. Our main result is Theorem 8.2 If y < 0 and x > y, then IED(Zt > x, mZ < y) = e2vy6-2IED(Zt < 2y - x + 2vt) = e2vyv-2N (2y - x + Vt 1 0- "It .

A quanto option is an option that whose pay-off is transformed into another currency at pre-determined rate. A multi-dimensional Brownian motion is a vector of processes which have jointly normal increments and is a Brownian motion in each dimension. Correlated Brownian motions can be constructed by adding together multiples of one-dimensional Brownian motions. The Ito calculus goes over to higher dimensions with the additional rule dWjdWk = pjkdt where Pjk is the correlation between Wj and Wk. When adding correlation Brownian motions we can find the volatility of the new process by treating the original processes as vectors. We can change the drift of a multi-dimensional Brownian motion by using Girsanov's theorem. 11.11 Exercises 281 No arbitrage will occur if and only if the discounted price processes can be made driftless by a change of measure.

If we interpret the correlation coefficient as being the cosine of the angle between the two Brownian motions, then this means that the new volatility is just the length of the vector obtained by summing the vectors for each Brownian motion. 266 Multiple sources of risk More generally, we could construct a Brownian motion from any vector a=(a1,...,ak) Ek=1 ajX( ). with a? = 1, by taking When we have a process driven by k > 2 Brownian motions, we obtain a similar expression to (11.20). The volatility becomes n Y" Ors 6j Pig N i,J=1 and we can write dYt = µdt + adW, (11.22) for a Brownian motion W constructed from the old one. We can similarly regard our processes as vectors in 1R which add according to their directions. Example 11.1 Suppose the stocks Xt and Yt follow correlated geometric Brownian motions. Show that XtYt also follows a geometric Brownian motion and compute its drift and volatility. Solution We write dXt = aXtdt + o XtdWW 1), dYt = ,BYtdt + vYdWt(2), and take the correlation coefficient to be p. We compute d(XtYt) = XtdYt + YtdXt + dXt.dYt, = XtYt (f3dt + vdW 2) + adt + vdWr 1) + avpdt) , = XtYt ((a +,B + QVp)dt + o'dW(1) + vdWr2)) .

Monte Carlo Simulation and Finance by Don L. McLeish

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Black-Scholes formula, Brownian motion, capital asset pricing model, compound rate of return, discrete time, distributed generation, finite state, frictionless, frictionless market, implied volatility, incomplete markets, invention of the printing press, martingale, p-value, random walk, Sharpe ratio, short selling, stochastic process, stochastic volatility, the market place, transaction costs, value at risk, Wiener process, zero-coupon bond

To motivate this family of distributions, let us GENERATING RANDOM NUMBERS FROM NON-UNIFORM CONTINUOUS DISTRIBUTIONS159 250 200 150 100 50 0 -50 -100 -150 -200 -250 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Figure 3.18: A Symmetric Stable Random Walk with index α = 1.7 suppose that stock returns follow a Brownian motion process but with respect to a random time scale possibly dependent on volume traded and other external factors independent of the Brownian motion itself. After one day, say, the return on the stock is the value of the Brownian motion process at a random time, τ, independent of the Brownian motion. Assume that this random time has the Inverse Gaussian distribution having probability density function (θ − t)2 θ exp{− } g(t) = √ 2c2 t c 2πt3 (3.21) for parameters θ > 0, c > 0. This is the distribution of a first passage time for Brownian motion. In particular consider a Brownian motion process B(t) having drift 1 and diffusion coefficient c. Such a process is the solution to the stochastic differential equation dB(t) = dt + cdW (t), B(0) = 0.

The high dm is generated by moving horizontally to the right an even number of steps until just before exiting the histogram. This is above the value d2m−u and dm is between du and d2m−u . A similar result is available for Brownian motion and Geometric Brownian motion. A justification of these results can be made by taking a limit in the discrete case as the time steps and the distances dj − dj−1 all approach zero. If we do this, the parameter θ is analogous to the drift of the Brownian motion. The result for Brownian motion is as follows: Theorem 44 Suppose St is a Brownian motion process dSt = µdt + σdWt , S0 = 0, ST = C, H = max{St ; 0 · t · T } and L = min{St ; 0 · t · T }. If f0 denotes the Normal(0,σ 2 T ) probability density function, the distribution of SIMULATING BARRIER AND LOOKBACK OPTIONS 277 C under drift µ = 0, then f0 (2H − C) is distributed as U [0, 1] independently of C, f0 (C) f0 (2L − C) UL = is distributed as U [0, 1] independently of C. f0 (C) 1 ZH = H(H − C) is distributed as Exponential ( σ 2 T ) independently of C, 2 1 2 ZL = L(L − C) is distributed as Exponential ( σ T )independently of C. 2 UH = We will not prove this result since it is a special case of Theorem 46 below.

The vertical √ scale is to be decreased by a factor 1/ n and the horizontal scale by a factor n−1 . The theorem concludes that the sequence of processes 1 Yn (t) = √ Snt n converges weakly to a standard Brownian motion process as n → ∞. In practice this means that a process with independent stationary increments tends to look like a Brownian motion process. As we shall see, there is also a wide variety of non-stationary processes that can be constructed from the Brownian motion process by integration. Let us use the above limiting result to render some of the properties of the Brownian motion more plausible, since a serious proof is beyond our scope. Consider the question of continuity, for example. Since Pn(t+h) |Yn (t + h) − Yn (t)| ≈ | √1n i=nt Xi | and this is the absolute value of an asymptotically normally(0, h) random variable by the central limit theorem, it is plausible that the limit as h → 0 is zero so the function is continuous at t.


pages: 443 words: 51,804

Handbook of Modeling High-Frequency Data in Finance by Frederi G. Viens, Maria C. Mariani, Ionut Florescu

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algorithmic trading, asset allocation, automated trading system, backtesting, Black-Scholes formula, Brownian motion, business process, continuous integration, corporate governance, discrete time, distributed generation, fixed income, Flash crash, housing crisis, implied volatility, incomplete markets, linear programming, mandelbrot fractal, market friction, market microstructure, martingale, Menlo Park, p-value, pattern recognition, performance metric, principal–agent problem, random walk, risk tolerance, risk/return, short selling, statistical model, stochastic process, stochastic volatility, transaction costs, value at risk, volatility smile, Wiener process

In this chapter, we consider the continuous-time long-memory stochastic volatility (LMSV) model by Comte and Renault (1998): If Xt are the log-returns of the price process St and Yt is the volatility process, then ⎧ ⎨ dXt ⎩ dYt σ 2 (Yt ) = μ− dt + σ (Yt ) dWt , 2 = α Yt dt + β dBtH , (8.1) where Wt is a standard Brownian motion and BtH is a fractional Brownian motion with Hurst index H ∈ (0, 1]. The fractional Brownian motion (fBm) with Hurst parameter H ∈ (0, 1] is a Gaussian process with almost surely continuous paths and covariance structure given by Cov(BtH , BsH ) = 1 2H |t| + |s|2H − |t − s|2H . 2 For H = 1/2 the process is the well-known standard Brownian motion. Formally, we say that a process exhibits long-range dependence when the series of the autocorrelation function is nonsummable, that is +∞ n=1 ρ(n) = +∞. 8.1 Introduction 221 From the covariance function of the fractional Brownian motion, we can easily deduce that the autocorrelation function of the increments of fBm is of order n2H −2 .

Dayanik and Karatzas (2003), Proposition 5.7 STANDING ASSUMPTION 11.15 l0 = x ↓ 0 h+ (x) h+ (x) < ∞, and l = x ↑ ∞ . ∞ x ρ− x ρ+ Let us denote by τx inf {t ≥ 0 / Y (t) = x}, x > 0, the first hitting time of level x. The reduction of the optimal stopping problem to the Brownian motion case has been studied by Dayanik and Karatzas in the case when the diffusion was driven by one-dimensional Brownian motion. Their results hold also for the case in which we have a m-dimensional Brownian motion with the only modification in the equation solved by the Green functions ψ and ϕ. Still, the problem is solved explicitly for the Brownian motion case by using a graphical method. By taking advantage of the theory developed in Dayanik and Karatzas (2003), in terms of the existence of an optimal stopping time and provided that we can either solve or determine the shape of intervals that form C0 {y > 0/Lg(y) > 0}, (11.59) then the value function is the supremum over stopping times which are exit times from open intervals that contain C0 .

In fact, the parameter α of the Levy distribution is inversely proportional to the Hurst parameter. The Hurst parameter is an indicator of the memory effects coming from the fractional Brownian motion, which has correlated increments. Furthermore, the TLF maintains statistical properties that are indistinguishable from the Levy flights [15]. 6.2.2 RESCALED RANGE ANALYSIS Hurst [27] initially developed the Rescaled range analysis (R/S analysis). He observed many natural phenomena that followed a biased random walk, that is, every phenomenon showed a pattern. He measured the trend using an exponent now called the Hurst exponent. Mandelbrot [28,29] later introduced a generalized form of the Brownian motion model, the fractional Brownian motion to model the Hurst effect. The numerical procedure to estimate the Hurst exponent H by using the R/S analysis is presented next (for more details, please see [27] and references therein). 1.


pages: 364 words: 101,286

The Misbehavior of Markets by Benoit Mandelbrot

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Albert Einstein, asset allocation, Augustin-Louis Cauchy, Benoit Mandelbrot, Big bang: deregulation of the City of London, Black-Scholes formula, British Empire, Brownian motion, buy low sell high, capital asset pricing model, carbon-based life, discounted cash flows, diversification, double helix, Edward Lorenz: Chaos theory, Elliott wave, equity premium, Eugene Fama: efficient market hypothesis, Fellow of the Royal Society, full employment, Georg Cantor, Henri Poincaré, implied volatility, index fund, informal economy, invisible hand, John von Neumann, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, market bubble, market microstructure, new economy, paper trading, passive investing, Paul Lévy, Plutocrats, plutocrats, price mechanism, quantitative trading / quantitative finance, Ralph Nelson Elliott, RAND corporation, random walk, risk tolerance, Robert Shiller, Robert Shiller, short selling, statistical arbitrage, statistical model, Steve Ballmer, stochastic volatility, transfer pricing, value at risk, volatility smile

Instead, it is best to go beyond cartoons. My current best model of how a market works is fractional Brownian motion of multifractal time. It has been called the Multifractal Model of Asset Returns. The basic ideas are similar to the cartoon versions above—though far more intricate, mathematically. The cartoon of Brownian motion gets replaced by an equation that a computer can calculate. The trading-time process is expressed by another mathematical function, called f(α), that can be tuned to fit a wide range of market behavior. My model redistributes time. It compresses it in some places, stretches it out in others. The result appears very wild, very random. The two functions, of time and Brownian motion, work together in what mathematicians call a compound manner: Price is a function of trading time, which in turn is a function of clock time.

Here, major news—approval of a medicine by the Food and Drug Administration, an unexpected takeover offer, or a windfall legal victory—caused market indigestion; sell and buy orders did not match, and market-makers had to raise or lower their price quotes until they did. To cope, some exchanges license “specialist” broker-dealers to step into the breach and trade when others will not. These specialists, while risking much, also profit greatly. Discontinuity, far from being an anomaly best ignored, is an essential ingredient of markets that helps set finance apart from the natural sciences. 4. Assumption: Price changes follow a Brownian motion. Theory: Brownian motion, again, is a term borrowed from physics for the motion of a molecule in a uniformly warm medium. Bachelier had suggested that this process can also describe price variation. Several critical assumptions come together in this idea. First, independence: Each change in price—whether a five-cent uptick or a $26 collapse—appears independently from the last, and price changes last week or last year do not influence those today.

By repeating this process over and over, a jagged, complex chart gradually appeared. By careful design, the specific kind of chart shown before was of a Brownian motion—the standard model underlying conventional financial theory. What made it so was the specific shape of the generator: Starting at the point (0, 0), it rose to the point (4/9, 2/3), fell to the point (5/9, 1/3), and ended up at (1, 1). A key observation regards the size of the three segments of the generator. Their widths were 4/9, 1/9, 4/9. The heights: 2/3, -1/3 (minus, because the line falls), and 2/3. Look closely at those six numbers. Each width is the square of each height. It is a nice, tidy relationship—just the kind of thing you would expect from a well-mannered Brownian motion. A cartoon of discontinuity. There are many ways to illustrate the crucial concepts of fat tails and discontinuity—and this one employs the kind of fractal process used earlier in this book.


pages: 313 words: 34,042

Tools for Computational Finance by Rüdiger Seydel

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bioinformatics, Black-Scholes formula, Brownian motion, continuous integration, discrete time, implied volatility, incomplete markets, interest rate swap, linear programming, London Interbank Offered Rate, mandelbrot fractal, martingale, random walk, stochastic process, stochastic volatility, transaction costs, value at risk, volatility smile, Wiener process, zero-coupon bond

. — The Example 1.15 with a system of three SDEs is taken from [HPS92]. [KP92] in Section 4.4 gives a list of SDEs that are analytically solvable or reducible. The model of a geometric Brownian motion of equation (1.33) is the classical model describing the dynamics of stock prices. It goes back to Samuelson (1965; Nobel Prize in economics in 1970). Already in 1900 Bachelier had suggested to model stock prices with Brownian motion. Bachelier used the arithmetic version, which can be characterized by replacing the lefthand side of (1.33) by the absolute change dS. This amounts to the process St = S0 + µt + σWt . Here the stock price can become negative. Main advantages of the geometric Brownian motion are the success of the approaches of Black, Merton and Scholes, which is based on that motion, and the existence of moments (as the expectation).

. = equal except for rounding errors ≡ identical =⇒ implication ⇐⇒ equivalence Landau-symbol: for h → 0 O(hk ) is bounded f (h) = O(hk ) ⇐⇒ fh(h) k normal distributed with expectation µ and variance σ 2 ∼ N (µ, σ 2 ) ∼ U[0, 1] uniformly distributed on [0, 1] XVIII Notations ∆t tr C 0 [a, b] ∈ C k [a, b] D ∂D L2 H [0, 1]2 Ω f + := max{f, 0} u̇ small increment in t transposed; Atr is the matrix where the rows and columns of A are exchanged. set of functions that are continuous on [a, b] k-times continuously differentiable set in IRn or in the complex plane, D̄ closure of D, D◦ interior of D boundary of D set of square-integrable functions Hilbert space, Sobolev space (Appendix C3) unit square sample space (in Appendix B1) time derivative du dt of a function u(t) integers: i, j, k, l, m, n, M, N, ν various variables: Xt , X, X(t) Wt y(x, τ ) w h ϕ ψ 1D random variable Wiener process, Brownian motion (Definition 1.7) solution of a partial differential equation for (x, τ ) approximation of y discretization grid size basis function (Chapter 5) test function (Chapter 5) indicator function: = 1 on D, = 0 elsewhere. abbreviations: BDF CFL Dow FTBS FTCS GBM MC ODE OTC PDE PIDE PSOR QMC SDE SOR Backward Difference Formula, see Section 4.2.1 Courant-Friedrichs-Lewy, see Section 6.5.1 Dow Jones Industrial Average Forward Time Backward Space, see Section 6.5.1 Forward Time Centered Space, see Section 6.4.2 Geometric Brownian Motion, see (1.33) Monte Carlo Ordinary Differential Equation Over The Counter Partial Differential Equation Partial Integro-Differential Equation Projected Successive Overrelaxation Quasi Monte Carlo Stochastic Differential Equation Successive Overrelaxation Notations TVD i.i.d. inf sup supp(f ) XIX Total Variation Diminishing independent and identical distributed infimum, largest lower bound of a set of numbers supremum, least upper bound of a set of numbers support of a function f : {x ∈ D : f (x) = 0} hints on the organization: (2.6) (A4.10) −→ number of equation (2.6) (The first digit in all numberings refers to the chapter.) equation in Appendix A; similarly B, C, D hint (for instance to an exercise) Chapter 1 Modeling Tools for Financial Options 1.1 Options What do we mean by option?

The ∆ of (1.16) is the hedge parameter delta, which eliminates the risk exposure of our portfolio caused by the written option. In multi-period models and continuous models ∆ must be adapted dynamically. The general definition is ∂V (S, t) ; ∆ = ∆(S, t) = ∂S the expression (1.16) is a discretized version. 1.6 Stochastic Processes Brownian motion originally meant the erratic motion of a particle (pollen) on the surface of a fluid, caused by tiny impulses of molecules. Wiener suggested a mathematical model for this motion, the Wiener process. But earlier Bachelier had applied Brownian motion to model the motion of stock prices, which instantly respond to the numerous upcoming informations similar as pollen react to the impacts of molecules. The illustration of the Dow in Figure 1.14 may serve as motivation. A stochastic process is a family of random variables Xt , which are defined for a set of parameters t (−→ Appendix B1).


pages: 320 words: 33,385

Market Risk Analysis, Quantitative Methods in Finance by Carol Alexander

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asset allocation, backtesting, barriers to entry, Brownian motion, capital asset pricing model, constrained optimization, credit crunch, Credit Default Swap, discounted cash flows, discrete time, diversification, diversified portfolio, en.wikipedia.org, implied volatility, interest rate swap, market friction, market microstructure, p-value, performance metric, quantitative trading / quantitative finance, random walk, risk tolerance, risk-adjusted returns, risk/return, Sharpe ratio, statistical arbitrage, statistical model, stochastic process, stochastic volatility, transaction costs, value at risk, volatility smile, Wiener process, yield curve

The process Wt is called a Wiener process, also called a Brownian motion. It is a continuous process that has independent increments dWt and each increment has a normal distribution with mean 0 and variance dt.19 On adding uncertainty to the exponential price path (I.1.31) the price process (I.1.29) becomes dSt = dt + dWt (I.1.32) St This is an example of a diffusion process. Since the left-hand side has the proportional change in the price at time t, rather than the absolute change, we call (I.1.32) geometric Brownian motion. If the left-hand side variable were dSt instead, the process would be called arithmetic Brownian motion. The diffusion coefficient is the coefficient of dWt, which is a constant in the case of geometric Brownian motion. This constant is called the volatility of the process.

Probability and Statistics 139 Application of Itô’s lemma with f = ln S shows that a continuous time representation of geometric Brownian motion that is equivalent to the geometric Brownian motion (I.3.143) but is translated into a process for log prices is the arithmetic Brownian motion, d ln St = − 21 2 dt + dWt (I.3.145) We already know what a discretization of (I.3.145) looks like. The change in the log price is the log return, so using the standard discrete time notation Pt for a price at time t we have d ln St → ln Pt Hence the discrete time equivalent of (I.3.145) is ln Pt = + $t $t ∼ NID 0 2 (I.3.146) where = − 21 2 . This is equivalent to a discrete time random walk model for the log prices, i.e. ln Pt = + ln Pt−1 + $t $t ∼ NID 0 2 (I.3.147) To summarize, the assumption of geometric Brownian motion for prices in continuous time is equivalent to the assumption of a random walk for log prices in discrete time.

A Wiener process, also called a Brownian motion, describes the stochastic part when the process does not jump. Thus a Wiener process is a continuous process with stationary, independent normally distributed increments. The increments are normally distributed so we often use any of the notations Wt Bt or Zt for such a process. The increments of the process are the total change in the process over an infinitesimally small time period; these are denoted dWt dBt or dZt, with EdW = 0 and VdW = dt Now we are ready to write the equation for the dynamics of a continuous time stochastic process X t as the following SDE: dXt = dt + dZt (I.3.141) where is called the drift of the process and is called the process volatility. The model (I.3.141) is called arithmetic Brownian motion. Arithmetic Brownian motion is the continuous time version of a random walk.


pages: 819 words: 181,185

Derivatives Markets by David Goldenberg

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Black-Scholes formula, Brownian motion, capital asset pricing model, commodity trading advisor, compound rate of return, conceptual framework, Credit Default Swap, discounted cash flows, discrete time, diversification, diversified portfolio, en.wikipedia.org, financial innovation, fudge factor, implied volatility, incomplete markets, interest rate derivative, interest rate swap, law of one price, locking in a profit, London Interbank Offered Rate, Louis Bachelier, margin call, market microstructure, martingale, Norbert Wiener, price mechanism, random walk, reserve currency, risk/return, riskless arbitrage, Sharpe ratio, short selling, stochastic process, stochastic volatility, time value of money, transaction costs, volatility smile, Wiener process, Y2K, yield curve, zero-coupon bond

398 11.7 Further Implications of European Put-Call Parity 11.7.1 Synthesizing Forward Contract from Puts and Calls 399 399 11.8 Financial Innovation using European Put-Call Parity 401 11.8.1 Generalized Forward Contracts 401 11.8.2 American Put-Call Parity (No Dividends) 403 11.9 Postscript on ROP CHAPTER 12 OPTION TRADING STRATEGIES, PART 2 405 415 12.1 Generating Synthetic Option Strategies from European Put-Call Parity 416 12.2 The Covered Call Hedging Strategy 419 12.2.1 Three Types Of Covered Call Writes 420 DETAILED CONTENTS xvii 12.2.2 Economic Interpretation of the Covered Call Strategy 12.3 The Protective Put Hedging Strategy 426 427 12.3.1 Puts as Insurance 427 12.3.2 Economic Interpretation of the Protective Put Strategy 429 CHAPTER 13 MODEL-BASED OPTION PRICING IN DISCRETE TIME, PART 1: THE BINOMIAL OPTION PRICING MODEL (BOPM, N=1) 435 13.1 The Objective of Model-Based Option Pricing (MBOP) 437 13.2 The Binomial Option Pricing Model, Basics 437 13.2.1 Modeling Time in a Discrete Time Framework 437 13.2.2 Modeling the Underlying Stock Price Uncertainty 438 13.3 The Binomial Option Pricing Model, Advanced 440 13.3.1 Path Structure of the Binomial Process, Total Number of Price Paths 440 13.3.2 Path Structure of the Binomial Process, Total Number of Price Paths Ending at a Specific Terminal Price 442 13.3.3 Summary of Stock Price Evolution for the N-Period Binomial Process 444 13.4 Option Valuation for the BOPM (N=1) 445 13.4.1 Step 1, Pricing the Option at Expiration 445 13.4.2 Step 2, Pricing the Option Currently (time t=0) 446 13.5 Modern Tools for Pricing Options 448 13.5.1 Tool 1, The Principle of No-Arbitrage 448 13.5.2 Tool 2, Complete Markets or Replicability, and a Rule of Thumb 449 13.5.3 Tool 3, Dynamic and Static Replication 450 xviii DETAILED CONTENTS 13.5.4 Relationships between the Three Tools 13.6 Synthesizing a European Call Option 450 453 13.6.1 Step 1, Parameterization 454 13.6.2 Step 2, Defining the Hedge Ratio and the Dollar Bond Position 455 13.6.3 Step 3, Constructing the Replicating Portfolio 456 13.6.4 Step 4, Implications of Replication 462 13.7 Alternative Option Pricing Techniques 464 13.8 Appendix: Derivation of the BOPM (N=1) as a Risk-Neutral Valuation Relationship 467 CHAPTER 14 OPTION PRICING IN DISCRETE TIME, PART 2: DYNAMIC HEDGING AND THE MULTI-PERIOD BINOMIAL OPTION PRICING MODEL, N>1 14.1 Modeling Time and Uncertainty in the BOPM, N>1 473 475 14.1.1 Stock Price Behavior, N=2 475 14.1.2 Option Price Behavior, N=2 476 14.2 Hedging a European Call Option, N=2 477 14.2.1 Step 1, Parameterization 477 14.2.2 Step 2, Defining the Hedge Ratio and the Dollar Bond Position 478 14.2.3 Step 3, Constructing the Replicating Portfolio 478 14.2.4 The Complete Hedging Program for the BOPM, N=2 484 14.3 Implementation of the BOPM for N=2 485 14.4 The BOPM, N>1 as a RNVR Formula 490 14.5 Multi-period BOPM, N>1: A Path Integral Approach 493 DETAILED CONTENTS xix 14.5.1 Thinking of the BOPM in Terms of Paths 493 14.5.2 Proof of the BOPM Model for general N 499 CHAPTER 15 EQUIVALENT MARTINGALE MEASURES: A MODERN APPROACH TO OPTION PRICING 15.1 Primitive Arrow–Debreu Securities and Option Pricing 507 508 15.1.1 Exercise 1, Pricing B(0,1) 510 15.1.2 Exercise 2, Pricing ADu() and ADd() 511 15.2 Contingent Claim Pricing 514 15.2.1 Pricing a European Call Option 514 15.2.2 Pricing any Contingent Claim 515 15.3 Equivalent Martingale Measures (EMMs) 517 15.3.1 Introduction and Examples 517 15.3.2 Definition of a Discrete-Time Martingale 521 15.4 Martingales and Stock Prices 15.4.1 The Equivalent Martingale Representation of Stock Prices 15.5 The Equivalent Martingale Representation of Option Prices 521 524 526 15.5.1 Discounted Option Prices 527 15.5.2 Summary of the EMM Approach 528 15.6 The Efficient Market Hypothesis (EMH), A Guide To Modeling Prices 529 15.7 Appendix: Essential Martingale Properties 533 CHAPTER 16 OPTION PRICING IN CONTINUOUS TIME 539 16.1 Arithmetic Brownian Motion (ABM) 540 16.2 Shifted Arithmetic Brownian Motion 541 16.3 Pricing European Options under Shifted Arithmetic Brownian Motion with No Drift (Bachelier) 542 xx DETAILED CONTENTS 16.3.1 Theory (FTAP1 and FTAP2) 542 16.3.2 Transition Density Functions 543 16.3.3 Deriving the Bachelier Option Pricing Formula 547 16.4 Defining and Pricing a Standard Numeraire 551 16.5 Geometric Brownian Motion (GBM) 553 16.5.1 GBM (Discrete Version) 553 16.5.2 Geometric Brownian Motion (GBM), Continuous Version 559 16.6 Itô’s Lemma 562 16.7 Black–Scholes Option Pricing 566 16.7.1 Reducing GBM to an ABM with Drift 567 16.7.2 Preliminaries on Generating Unknown Risk-Neutral Transition Density Functions from Known Ones 570 16.7.3 Black–Scholes Options Pricing from Bachelier 571 16.7.4 Volatility Estimation in the Black–Scholes Model 582 16.8 Non-Constant Volatility Models 585 16.8.1 Empirical Features of Volatility 585 16.8.2 Economic Reasons for why Volatility is not Constant, the Leverage Effect 586 16.8.3 Modeling Changing Volatility, the Deterministic Volatility Model 586 16.8.4 Modeling Changing Volatility, Stochastic Volatility Models 16.9 Why Black–Scholes is Still Important CHAPTER 17 RISK-NEUTRAL VALUATION, EMMS, THE BOPM, AND BLACK–SCHOLES 17.1 Introduction 17.1.1 Preliminaries on FTAP1 and FTAP2 and Navigating the Terminology 587 588 595 596 596 DETAILED CONTENTS xxi 17.1.2 Pricing by Arbitrage and the FTAP2 597 17.1.3 Risk-Neutral Valuation without Consensus and with Consensus 598 17.1.4 Risk-Neutral Valuation without Consensus, Pricing Contingent Claims with Unhedgeable Risks 599 17.1.5 Black–Scholes’ Contribution 601 17.2 Formal Risk-Neutral Valuation without Replication 601 17.2.1 Constructing EMMs 601 17.2.2 Interpreting Formal Risk-Neutral Probabilities 602 17.3 MPRs and EMMs, Another Version of FTAP2 605 17.4 Complete Risk-Expected Return Analysis of the Riskless Hedge in the (BOPM, N=1) 607 17.4.1 Volatility of the Hedge Portfolio 608 17.4.2 Direct Calculation of S 611 17.4.3 Direct Calculation of C 612 17.4.4 Expected Return of the Hedge Portfolio 616 17.5 Analysis of the Relative Risks of the Hedge Portfolio’s Return 618 17.5.1 An Initial Look at Risk Neutrality in the Hedge Portfolio 618 17.5.2 Role of the Risk Premia for a Risk-Averse Investor in the Hedge Portfolio 620 17.6 Option Valuation Index 624 17.6.1 Some Manipulations 624 17.6.2 Option Valuation Done Directly by a Risk-Averse Investor 626 17.6.3 Option Valuation for the Risk-Neutral Investor 631 637 This page intentionally left blank FIGURES 1.1 1.2 1.3 1.4 2.1 2.2 2.3 2.4 3.1 3.2 3.3 3.4 5.1 5.2 5.3 5.4 6.1 6.2 6.3 6.4 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 Canada/US Foreign Exchange Rate Intermediation by the Clearing House Offsetting Trades Gold Fixing Price in London Bullion Market (USD$) Graphical Method to Get Hedged Position Profits Payoff Per Share to a Long Forward Contract Payoff Per Share to a Short Forward Contract Profits per bu. for the Unhedged Position Profits Per Share to a Naked Long Spot Position Payoffs Per Share to a Naked Long Spot Position Payoffs (=Profits) Per Share to a Naked Long Forward Position Payoffs Per Share to a Naked Long Spot Position and to a Naked Long Forward Position Order Flow Process (Pit Trading) The Futures Clearing House Offsetting Trades Overall Profits for Example 2 Long vs.

We used the fact that X1() is independent of W0 in the fourth equality. Our conclusion is that the property E(W1()|W0)=W0 holds. CHAPTER 16 OPTION PRICING IN CONTINUOUS TIME 16.1 Arithmetic Brownian Motion (ABM) 540 16.2 Shifted Arithmetic Brownian Motion 541 16.3 Pricing European Options under Shifted Arithmetic Brownian Motion with No Drift (Bachelier) 542 16.3.1 Theory (FTAP1 and FTAP2) 542 16.3.2 Transition Density Functions 543 16.3.3 Deriving the Bachelier Option Pricing Formula 547 16.4 Defining and Pricing a Standard Numeraire 551 16.5 Geometric Brownian Motion (GBM) 553 16.5.1 GBM (Discrete Version) 553 16.5.2 Geometric Brownian Motion (GBM), Continuous Version 559 16.6 Itô’s Lemma 562 16.7 Black–Scholes Option Pricing 566 16.7.1 Reducing GBM to an ABM with Drift 567 16.7.2 Preliminaries on Generating Unknown Risk-Neutral Transition Density Functions from Known Ones 570 16.7.3 Black–Scholes Options Pricing from Bachelier 571 16.7.4 Volatility Estimation in the Black–Scholes Model 582 16.8 Non-Constant Volatility Models 585 16.8.1 Empirical Features of Volatility 585 16.8.2 Economic Reasons for why Volatility is not Constant, the Leverage Effect 586 540 OPTIONS 16.8.3 Modeling Changing Volatility, the Deterministic Volatility Model 586 16.8.4 Modeling Changing Volatility, Stochastic Volatility Models 16.9 Why Black–Scholes Is Still Important 587 588 In this chapter we are going to give an introduction to continuous-time finance.

Black–Scholes (1973), which is a continuous time, continuous state space model even shows up in some jump option pricing models, such as Merton’s (1976) jump model. Thus, Black–Scholes may indeed survive as a component of some option pricing models. We should probably keep it around for these reasons. n n n 590 n OPTIONS KEY CONCEPTS 1. Arithmetic Brownian Motion (ABM). 2. Shifted Arithmetic Brownian Motion. 3. Pricing European Options under Shifted Arithmetic Brownian Motion (Bachelier). 4. Theory (FTAP1 and FTAP2). 5. Transition Density Functions. 6. Deriving the Bachelier Option Pricing Formula. 7. Defining and Pricing a Standard Numeraire. 8. Geometric Brownian Motion (GBM). 9. GBM (Discrete Version). 10. Geometric Brownian Motion (GBM), Continuous Version. 11. Itô’s Lemma. 12. Black–Scholes Option Pricing. 13. Reducing GBM to an ABM with Drift. 14. Preliminaries on Risk-Neutral Transition Density Functions. 15. Black–Scholes Pricing from Bachelier. 16.


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Frequently Asked Questions in Quantitative Finance by Paul Wilmott

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Albert Einstein, asset allocation, Black-Scholes formula, Brownian motion, butterfly effect, capital asset pricing model, collateralized debt obligation, Credit Default Swap, credit default swaps / collateralized debt obligations, delta neutral, discrete time, diversified portfolio, Emanuel Derman, Eugene Fama: efficient market hypothesis, fixed income, fudge factor, implied volatility, incomplete markets, interest rate derivative, interest rate swap, iterative process, London Interbank Offered Rate, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, margin call, market bubble, martingale, Norbert Wiener, quantitative trading / quantitative finance, random walk, regulatory arbitrage, risk/return, Sharpe ratio, statistical arbitrage, statistical model, stochastic process, stochastic volatility, transaction costs, urban planning, value at risk, volatility arbitrage, volatility smile, Wiener process, yield curve, zero-coupon bond

Short Answer Girsanov’s theorem is the formal concept underlying the change of measure from the real world to the risk-neutral world. We can change from a Brownian motion with one drift to a Brownian motion with another. Example The classical example is to start withdS = µS dt + σ S dWt with W being Brownian motion under one measure (the real-world measure) and converting it to under a different, the risk-neutral, measure. Long Answer First a statement of the theorem. Let Wt be a Brownian motion with measure and sample space Ω. If γt is a previsible process satisfying the constraint then there exists an equivalent measure on Ω such that is a Brownian motion. It will be helpful if we explain some of the more technical terms in this theorem. Sample space: All possible future states or outcomes.

Figure 2-5: Certainty equivalent as a function of the risk-aversion parameter for example in the text. References and Further Reading Ingersoll, JE Jr 1987 Theory of Financial Decision Making. Rowman & Littlefield What is Brownian Motion and What are its Uses in Finance? Short Answer Brownian Motion is a stochastic process with stationary independent normally distributed increments and which also has continuous sample paths. It is the most common stochastic building block for random walks in finance. Example Pollen in water, smoke in a room, pollution in a river, are all examples of Brownian motion. And this is the common model for stock prices as well. Long Answer Brownian motion (BM) is named after the Scottish botanist who first described the random motions of pollen grains suspended in water. The mathematics of this process were formalized by Bachelier, in an option-pricing context, and by Einstein.

This idea of the random walk has permeated many scientific fields and is commonly used as the model mechanism behind a variety of unpredictable continuous-time processes. The lognormal random walk based on Brownian motion is the classical paradigm for the stock market. See Brown (1827). 1900 Bachelier Louis Bachelier was the first to quantify the concept of Brownian motion. He developed a mathematical theory for random walks, a theory rediscovered later by Einstein. He proposed a model for equity prices, a simple normal distribution, and built on it a model for pricing the almost unheard of options. His model contained many of the seeds for later work, but lay ‘dormant’ for many, many years. It is told that his thesis was not a great success and, naturally, Bachelier’s work was not appreciated in his lifetime. See Bachelier (1995). 1905 Einstein Albert Einstein proposed a scientific foundation for Brownian motion in 1905. He did some other clever stuff as well.


pages: 338 words: 106,936

The Physics of Wall Street: A Brief History of Predicting the Unpredictable by James Owen Weatherall

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Albert Einstein, algorithmic trading, Antoine Gombaud: Chevalier de Méré, Asian financial crisis, bank run, Benoit Mandelbrot, Black Swan, Black-Scholes formula, Bonfire of the Vanities, Bretton Woods, Brownian motion, butterfly effect, capital asset pricing model, Carmen Reinhart, Claude Shannon: information theory, collateralized debt obligation, collective bargaining, dark matter, Edward Lorenz: Chaos theory, Emanuel Derman, Eugene Fama: efficient market hypothesis, financial innovation, George Akerlof, Gerolamo Cardano, Henri Poincaré, invisible hand, Isaac Newton, iterative process, John Nash: game theory, Kenneth Rogoff, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, martingale, new economy, Paul Lévy, prediction markets, probability theory / Blaise Pascal / Pierre de Fermat, quantitative trading / quantitative finance, random walk, Renaissance Technologies, risk-adjusted returns, Robert Gordon, Robert Shiller, Robert Shiller, Ronald Coase, Sharpe ratio, short selling, Silicon Valley, South Sea Bubble, statistical arbitrage, statistical model, stochastic process, The Chicago School, The Myth of the Rational Market, tulip mania, V2 rocket, volatility smile

Over the course of the next six years, French physicist Jean-Baptiste Perrin developed an experimental method to track particles suspended in a fluid with enough precision to show that they indeed followed paths of the sort Einstein predicted. These experiments were enough to persuade the remaining skeptics that atoms did indeed exist. Lucretius’s contribution, meanwhile, went largely unappreciated. The kind of paths that Einstein was interested in are examples of Brownian motion, named after Scottish botanist Robert Brown, who noted the random movement of pollen grains suspended in water in 1826. The mathematical treatment of Brownian motion is often called a random walk — or sometimes, more evocatively, a drunkard’s walk. Imagine a man coming out of a bar in Cancun, an open bottle of sunscreen dribbling from his back pocket. He walks forward for a few steps, and then there’s a good chance that he will stumble in one direction or another. He steadies himself, takes another step, and then stumbles once again.

They get interested in a stock, they make a lot of trades and send the volume of trades way up, and then they gradually stop paying attention and volume decreases. If you allow for variations in volume, you have to change the underlying assumptions of the random walk model, and you get a new, more accurate model of how stock prices evolve, which Osborne called the “extended Brownian motion” model. In the mid-sixties, Osborne and a collaborator showed that at any instant, the chances that a stock will go up are not necessarily the same as the chances that the stock will go down. This assumption, you’ll recall, was an essential part of the Brownian motion model, where a step in one direction is assumed to be just as likely as a step in the other. Osborne showed that if a stock went up a little bit, its next motion was much more likely to be a move back down than another move up. Likewise, if a stock went down, it was much more likely to go up in value in its next change.

Although discussing such debates is far from the scope of this book, I should note that the arguments offered here for how one should think of the status of mathematical models in finance are closely connected to more general discussions concerning the status of mathematical or physical theories quite generally. “. . . named after Scottish botanist Robert Brown . . .”: Brown’s observations were published as Brown (1828). “The mathematical treatment of Brownian motion . . .”: More generally, Brownian motion is an example of a random or “stochastic” process. For an overview of the mathematics of stochastic processes, see Karlin and Taylor (1975, 1981). “. . . it was his 1905 paper that caught Perrin’s eye”: Einstein published four papers in 1905. One of them was the one I refer to here (Einstein 1905b), but the other three were equally remarkable. In Einstein (1905a), he first suggests that light comes in discrete packets, now called quanta or photons; in Einstein (1905c), he introduces his special theory of relativity; and in Einstein (1905d), he proposes the famous equation e = mc2


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Mathematics of the Financial Markets: Financial Instruments and Derivatives Modelling, Valuation and Risk Issues by Alain Ruttiens

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algorithmic trading, asset allocation, asset-backed security, backtesting, banking crisis, Black Swan, Black-Scholes formula, Brownian motion, capital asset pricing model, collateralized debt obligation, correlation coefficient, Credit Default Swap, credit default swaps / collateralized debt obligations, delta neutral, discounted cash flows, discrete time, diversification, fixed income, implied volatility, interest rate derivative, interest rate swap, margin call, market microstructure, martingale, p-value, passive investing, quantitative trading / quantitative finance, random walk, risk/return, Sharpe ratio, short selling, statistical model, stochastic process, stochastic volatility, time value of money, transaction costs, value at risk, volatility smile, Wiener process, yield curve, zero-coupon bond

Coming back to the starting point of our non-deterministic description of financial products, in Chapter 8, Section 8.2, we have defined the Brownian motion, or standard Wiener process (also called white noise) as per Eq. 8.2: where y(t) is distributed as (E = 0, V = 1), so that Z(t) is distributed as (E = 0, V = t), that is, with STD = √ t. Because of the nature of y(t), successive values of Z are independent; in discrete time, and abandoning the random subscript “∼”, we have where is a so-called “random number”, actually a number randomly selected from a normal density distribution. For two different times t and t′, the covariance between two Brownian motions is necessarily 0, that is (cf. Eq. 8.5), E[dZ(t).dZ(t′)] = 0. Now, we can generalize the Brownian motion to a fractional Brownian motion BH, H ∈ (0, 1) having as covariance function The parameter H is called the Hurst coefficient.5 As a particular case, if H = , covH(t, t′) = 0 and B1/2 is our standard Brownian motion: the corresponding time series is (pure) random.

Passing from discrete to continuous time, and thus from discrete time (or “finite”) intervals Δt to infinitely short, « infinitesimal » or « instantaneous » time intervals noted dt, Eq. 8.1 becomes (8.2) called a standard Wiener process, or a Brownian process or Brownian motion.1 This process is also called (although improperly2) white noise, by analogy with the very light but permanent scratching behind a sound produced electronically. From Eq. 8.2 we may deduct that the (t)s are independently distributed and stationary. They are normally distributed, with E = 0, V = dt (or STD = dt). Furthermore, (t) is distributed according to a Gaussian distribution of parameters E = 0, V = t (or STD = t). We see now the reason of the presence of a in Eq. 8.1 and 2: the process allows us to consider that it is the variance V of the process that is proportional to time. Formally speaking, a process (X(t), t ≥ 0) is a standard Wiener or Brownian motion if: P[X(0)] = 0: the Brownian motion starts from the origin, in t0 = 0; ∀ s ≤ t, X(t) − X(s) is a real variable, normally distributed, centered on its mean, and with a variance equal to (t − s): the successive increases of the process are stationary; ∀ n, ∀ ti, 0 ≤ t1… ≤ tn, the variables X(tn) − X(tn−1), …, X(t1) − X(t0), X(t0), are independent: the successive increases of the process are independent.

Contents Cover Series Title Page Copyright Dedication Foreword Main Notations Introduction Part I: The Deterministic Environment Chapter 1: Prior to the yield curve: spot and forward rates 1.1 INTEREST RATES, PRESENT AND FUTURE VALUES, INTEREST COMPOUNDING 1.2 DISCOUNT FACTORS 1.3 CONTINUOUS COMPOUNDING AND CONTINUOUS RATES 1.4 FORWARD RATES 1.5 THE NO ARBITRAGE CONDITION FURTHER READING Chapter 2: The term structure or yield curve 2.1 INTRODUCTION TO THE YIELD CURVE 2.2 THE YIELD CURVE COMPONENTS 2.3 BUILDING A YIELD CURVE: METHODOLOGY 2.4 AN EXAMPLE OF YIELD CURVE POINTS DETERMINATION 2.5 INTERPOLATIONS ON A YIELD CURVE FURTHER READING Chapter 3: Spot instruments 3.1 SHORT-TERM RATES 3.2 BONDS 3.3 CURRENCIES FURTHER READING Chapter 4: Equities and stock indexes 4.1 STOCKS VALUATION 4.2 STOCK INDEXES 4.3 THE PORTFOLIO THEORY FURTHER READING Chapter 5: Forward instruments 5.1 THE FORWARD FOREIGN EXCHANGE 5.2 FRAs 5.3 OTHER FORWARD CONTRACTS 5.4 CONTRACTS FOR DIFFERENCE (CFD) FURTHER READING Chapter 6: Swaps 6.1 DEFINITIONS AND FIRST EXAMPLES 6.2 PRIOR TO AN IRS SWAP PRICING METHOD 6.3 PRICING OF AN IRS SWAP 6.4 (RE)VALUATION OF AN IRS SWAP 6.5 THE SWAP (RATES) MARKET 6.6 PRICING OF A CRS SWAP 6.7 PRICING OF SECOND-GENERATION SWAPS FURTHER READING Chapter 7: Futures 7.1 INTRODUCTION TO FUTURES 7.2 FUTURES PRICING 7.3 FUTURES ON EQUITIES AND STOCK INDEXES 7.4 FUTURES ON SHORT-TERM INTEREST RATES 7.5 FUTURES ON BONDS 7.6 FUTURES ON CURRENCIES 7.7 FUTURES ON (NON-FINANCIAL) COMMODITIES FURTHER READING Part II: The Probabilistic Environment Chapter 8: The basis of stochastic calculus 8.1 STOCHASTIC PROCESSES 8.2 THE STANDARD WIENER PROCESS, OR BROWNIAN MOTION 8.3 THE GENERAL WIENER PROCESS 8.4 THE ITÔ PROCESS 8.5 APPLICATION OF THE GENERAL WIENER PROCESS 8.6 THE ITÔ LEMMA 8.7 APPLICATION OF THE ITô LEMMA 8.8 NOTION OF RISK NEUTRAL PROBABILITY 8.9 NOTION OF MARTINGALE ANNEX 8.1: PROOFS OF THE PROPERTIES OF dZ(t) ANNEX 8.2: PROOF OF THE ITÔ LEMMA FURTHER READING Chapter 9: Other financial models: from ARMA to the GARCH family 9.1 THE AUTOREGRESSIVE (AR) PROCESS 9.2 THE MOVING AVERAGE (MA) PROCESS 9.3 THE AUTOREGRESSION MOVING AVERAGE (ARMA) PROCESS 9.4 THE AUTOREGRESSIVE INTEGRATED MOVING AVERAGE (ARIMA) PROCESS 9.5 THE ARCH PROCESS 9.6 THE GARCH PROCESS 9.7 VARIANTS OF (G)ARCH PROCESSES 9.8 THE MIDAS PROCESS FURTHER READING Chapter 10: Option pricing in general 10.1 INTRODUCTION TO OPTION PRICING 10.2 THE BLACK–SCHOLES FORMULA 10.3 FINITE DIFFERENCE METHODS: THE COX–ROSS–RUBINSTEIN (CRR) OPTION PRICING MODEL 10.4 MONTE CARLO SIMULATIONS 10.5 OPTION PRICING SENSITIVITIES FURTHER READING Chapter 11: Options on specific underlyings and exotic options 11.1 CURRENCY OPTIONS 11.2 OPTIONS ON BONDS 11.3 OPTIONS ON INTEREST RATES 11.4 EXCHANGE OPTIONS 11.5 BASKET OPTIONS 11.6 BERMUDAN OPTIONS 11.7 OPTIONS ON NON-FINANCIAL UNDERLYINGS 11.8 SECOND-GENERATION OPTIONS, OR EXOTICS FURTHER READING Chapter 12: Volatility and volatility derivatives 12.1 PRACTICAL ISSUES ABOUT THE VOLATILITY 12.2 MODELING THE VOLATILITY 12.3 REALIZED VOLATILITY MODELS 12.4 MODELING THE CORRELATION 12.5 VOLATILITY AND VARIANCE SWAPS FURTHER READING Chapter 13: Credit derivatives 13.1 INTRODUCTION TO CREDIT DERIVATIVES 13.2 VALUATION OF CREDIT DERIVATIVES 13.3 CONCLUSION FURTHER READING Chapter 14: Market performance and risk measures 14.1 RETURN AND RISK MEASURES 14.2 VaR OR VALUE-AT-RISK FURTHER READING Chapter 15: Beyond the Gaussian hypothesis: potential troubles with derivatives valuation 15.1 ALTERNATIVES TO THE GAUSSIAN HYPOTHESIS 15.2 POTENTIAL TROUBLES WITH DERIVATIVES VALUATION FURTHER READING Bibliography Index For other titles in the Wiley Finance series please see www.wiley.com/finance This edition first published 2013 Copyright © 2013 Alain Ruttiens Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com.


pages: 206 words: 70,924

The Rise of the Quants: Marschak, Sharpe, Black, Scholes and Merton by Colin Read

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Albert Einstein, Black-Scholes formula, Bretton Woods, Brownian motion, capital asset pricing model, collateralized debt obligation, correlation coefficient, Credit Default Swap, credit default swaps / collateralized debt obligations, David Ricardo: comparative advantage, discovery of penicillin, discrete time, Emanuel Derman, en.wikipedia.org, Eugene Fama: efficient market hypothesis, financial innovation, fixed income, floating exchange rates, full employment, Henri Poincaré, implied volatility, index fund, Isaac Newton, John von Neumann, Joseph Schumpeter, Long Term Capital Management, Louis Bachelier, margin call, market clearing, martingale, means of production, moral hazard, naked short selling, price stability, principal–agent problem, quantitative trading / quantitative finance, RAND corporation, random walk, risk tolerance, risk/return, Ronald Reagan, shareholder value, Sharpe ratio, short selling, stochastic process, The Chicago School, the scientific method, too big to fail, transaction costs, tulip mania, Works Progress Administration, yield curve

He also allowed a drift of zero mean of the security price and assumed that the variance of the price drift is proportional to the length of time of the random walk. In combination, he had described what we now call a Weiner process. The Times 105 While Bachelier was the first to apply Brownian motion to finance, the methodology is now commonplace. The term “Brownian motion” originated in 1828 from the observations of the botanist Robert Brown, who discovered that pollen suspended in water seemed to experience unusual and random jumps when observed under a microscope. The renowned MIT mathematician Norbert Weiner described the mathematics of Brownian motion in his 1918 PhD thesis. Bachelier had already discovered this, though. His statement that stock prices could be modeled as a random walk according to a Weiner process was amenable to empirical verification. Alfred Cowles, who would found the Cowles Commission, and Herbert Jones explored and subsequently vindicated this notion that there is no memory effect in the price of stocks in a 1937 paper together.8 While the notion of the random walk has since been replaced with the less restrictive concept of a martingale process, much of finance pricing theory still retains the random walk because of its simple first and second moment characterization of price movements.

Alternative approaches Once Black and Scholes’ paper was published in the prestigious Journal of Political Economy, and with the opening of the CBOE, options pricing theory had arrived as the most sophisticated and potentially most valuable tool for financial market analysts. As theorists struggled to understand and interpret their result, and as Merton soon published his complementary work, a renewed interest developed in Bachelier’s work from 70 years earlier, and even Einstein’s theory of Brownian motion. Within a few years, Brownian motion, Markov processes, martingales, and stochastic calculus had begun to be integrated into the finance discipline. The quantitative school of finance had taken root. At that time, those most schooled in stochastic calculus were trained in physics and applied mathematics. With the advent of the statistical approach to physics that arose from theories of thermodynamics and quantum mechanics in the early twentieth century, physicists had become accustomed to the path of processes buffeted by random shocks.

It too is of a value that follows a Weiner process because all assets the manager uses to fund his or her portfolio would follow a Weiner process. Then, the difference between the proportional drift of the sum of assets S used to fund this portfolio and the portfolio payout V will also follow a Weiner process: dS S − dV V = (μ − α )dt + θdB, The Theory 155 where µ is the mean return on the funding portfolio, ␣ is the mean return on the payout portfolio, and the Brownian motion term at the end is a combination of the standard deviation on the funding portfolio and the underlying stock multiplied by the Brownian motion of the underlying asset. Merton then established that the tracking error on such a funding portfolio made up of market securities is uncorrelated with the tracking error on the underlying security. This is a consequence of the choice of a funding portfolio that minimizes its correlation with the tracking errors so that one could not capitalize on predictable differences.

Analysis of Financial Time Series by Ruey S. Tsay

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Asian financial crisis, asset allocation, Black-Scholes formula, Brownian motion, capital asset pricing model, compound rate of return, correlation coefficient, data acquisition, discrete time, frictionless, frictionless market, implied volatility, index arbitrage, Long Term Capital Management, market microstructure, martingale, p-value, pattern recognition, random walk, risk tolerance, short selling, statistical model, stochastic process, stochastic volatility, telemarketer, transaction costs, value at risk, volatility smile, Wiener process, yield curve

Furthermore, for any given time indexes 0 ≤ t1 < t2 < · · · < tk , the random vector (wt1 , wt2 , . . . , wtk ) follows a multivariate normal distribution. Finally, a Brownian motion is standard if w0 = 0 almost surely, µ = 0, and σ 2 = 1. Remark: An important property of Brownian motions is that their paths are not differentiable almost surely. In other words, for a standard Brownian motion wt , it can be shown that dwt /dt does not exist for all elements of except for elements in a subset 1 ⊂ such that P(1 ) = 0. As a result, we cannot use the usual intergation in calculus to handle integrals involving a standard Brownian motion when we consider the value of an asset over time. Another approach must be sought. This is the purpose of discussing Ito’s calculus in the next section. 6.2.2 Generalized Wiener Processes The Wiener process is a special stochastic process with zero drift and variance proportional to the length of time interval.

If {et } is a white noise series with finite moments of order slightly greater than 2, then the DF-statistic converges to a function of the standard Brownian motion as T → ∞; see Chan and Wei (1988) and Phillips (1987) for more information. If φ0 is zero but Eq. (2.36) is employed anyway, then the resulting t ratio for testing φ1 = 1 will converge to another nonstandard asymptotic distribution. In either case, simulation is used to obtain critical values of the test statistics; see Fuller (1976, Chapter 8) for selected critical values. Yet if φ0 = 0 and Eq. (2.36) is used, then the t ratio for testing φ1 = 1 is asymptotically normal. However, large sample sizes are needed for the asymptotic normal distribution to hold. Standard Brownian motion is introduced in Chapter 6. 2.8 SEASONAL MODELS Some financial time series such as quarterly earning per share of a company exhibits certain cyclical or periodic behavior.

Using the notation of the general Ito’s process in Eq. (6.2), we have µ(xt , t) = µxt and σ (xt , t) = σ xt , where xt = Pt . Such a special process is referred to as a geometric Brownian motion. We now apply the Ito’s lemma to obtain a continuous-time model for the logarithm of the stock price Pt . Let G(Pt , t) = ln(Pt ) be the log price of the underlying stock. Then we have ∂G 1 = , ∂ Pt Pt ∂G = 0, ∂t 1 −1 1 ∂2G = . 2 2 ∂ Pt 2 Pt2 Consequently, via Ito’s lemma, we obtain d ln(Pt ) = 1 1 −1 2 2 σ2 1 µPt + σ Pt dt + σ Pt dwt = µ − dt + σ dwt . Pt 2 Pt2 Pt 2 ITO ’ S LEMMA 229 This result shows that the logarithm of a price follows a generalized Wiener Process with drift rate µ − σ 2 /2 and variance rate σ 2 if the price is a geometric Brownian motion. Consequently, the change in logarithm of price (i.e., log return) between current time t and some future time T is normally distributed with mean (µ−σ 2 /2)(T − t) and variance σ 2 (T −t).


pages: 374 words: 114,600

The Quants by Scott Patterson

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Albert Einstein, asset allocation, automated trading system, Benoit Mandelbrot, Bernie Madoff, Bernie Sanders, Black Swan, Black-Scholes formula, Bonfire of the Vanities, Brownian motion, buttonwood tree, buy low sell high, capital asset pricing model, centralized clearinghouse, Claude Shannon: information theory, cloud computing, collapse of Lehman Brothers, collateralized debt obligation, Credit Default Swap, credit default swaps / collateralized debt obligations, diversification, Donald Trump, Doomsday Clock, Emanuel Derman, Eugene Fama: efficient market hypothesis, fixed income, Gordon Gekko, greed is good, Haight Ashbury, index fund, invention of the telegraph, invisible hand, Isaac Newton, job automation, John Nash: game theory, law of one price, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, margin call, merger arbitrage, NetJets, new economy, offshore financial centre, Paul Lévy, Ponzi scheme, quantitative hedge fund, quantitative trading / quantitative finance, race to the bottom, random walk, Renaissance Technologies, risk-adjusted returns, Rod Stewart played at Stephen Schwarzman birthday party, Ronald Reagan, Sergey Aleynikov, short selling, South Sea Bubble, speech recognition, statistical arbitrage, The Chicago School, The Great Moderation, The Predators' Ball, too big to fail, transaction costs, value at risk, volatility smile, yield curve, éminence grise

The formula has many components, one of which is the assumption that the future movement of a stock—its volatility—is random and leaves out the likelihood of large swings (see fat tails). Brownian motion: First described by Scottish botanist Robert Brown in 1827 when observing pollen particles suspended in water, Brownian motion is the seemingly random vibration of molecules. Mathematically, the motion is a random walk in which the future direction of the movement—left, right, up, down—is unpredictable. The average of the motion, however, can be predicted using the law of large numbers, and is visually captured by the bell curve or normal distribution. Quants use Brownian motion mathematics to predict the volatility of everything from the stock market to the risk of a multinational bank’s balance sheet. Credit default swap: Created in the early 1990s, these contracts essentially provide insurance on a bond or a bundle of bonds.

After testing a range of other plant specimens, even the ground dust of rocks, and observing similar herky-jerky motion, he concluded that he was observing a phenomenon that was completely and mysteriously random. (The mystery remained unsolved for decades, until Albert Einstein, in 1905, discovered that the strange movement, by then known as Brownian motion, was the result of millions of microscopic particles buzzing around in a frantic dance of energy.) The connection between Brownian motion and market prices was made in 1900 by a student at the University of Paris named Louis Bachelier. That year, he’d written a dissertation called “The Theory of Speculation,” an attempt to create a formula that would capture the movement of bonds on the Paris stock exchange. The first English translation of the essay, which had lapsed into obscurity until it resurfaced again in the 1950s, had been included in the book about the market’s randomness that Thorp had read in New Mexico.

It’s much more likely that the confused drunkard will sway randomly in many directions as the night progresses (samples that would fall in the middle of the curve) than that he will move continuously in a straight line, or spin in a circle (samples that would fall in the ends of the curve, commonly known as the tails of the distribution). In a thousand coin flips, it’s more likely that the sample will contain roughly five hundred heads and five hundred tails (falling in the curve’s middle) than nine hundred heads and one hundred tails (outer edge of the curve). Thorp, already well aware of Einstein’s 1905 discovery, was familiar with Brownian motion and rapidly grasped the connection between bonds and warrants. Indeed, it was in a way the same statistical rule that had helped Thorp win at blackjack: the law of large numbers (the more observations, the more coin flips, the greater the certainty of prediction). While he could never know if he’d win every hand at blackjack, he knew that over time he’d come out on top if he followed his card-counting strategy.


pages: 246 words: 16,997

Financial Modelling in Python by Shayne Fletcher, Christopher Gardner

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Brownian motion, discrete time, interest rate derivative, London Interbank Offered Rate, stochastic volatility, yield curve, zero day, zero-coupon bond

Throughout this section we denote the function of the one-dimensional Brownian motion4 X T by yT := f (X T ) and the filtratio at time t by Ft . A full mathematical definitio of Brownian motion can be found in [16] but for the purposes of what follows all we need to know is that X T − X t is independent of X t for t < T and is normally distributed with zero mean and variance T − t. The aim of this subsection is to explain how to compute the following conditional expectations: yt := E[yT |Ft ] yt+ := E[max(yT , 0)|Ft ] (4.42) (4.43) Because the increments of a Brownian motion are independent of each other, the above conditional expectations can be written as yt (x) = E[ f (x + X T − X t )|xt = x] yt+ (x) = E[max( f (x + X T − X t ), 0)|xt = x] (4.44) (4.45) We donote the discrete grid of states for the Brownian motion increment X T − X t by xtT .

In the case of the rollback method the integrator is simply the integral member function of the distribution class represented by ftT, and in the case of the rollback max method the integrator is the integral max member function of ftT. class semi analytic domain integrator: def 4 create cached moments(self, x, f): In 1828 the Scottish botanist Robert Brown observed that pollen grains suspended in liquid performed an irregular motion – Brownian motion. 58 Financial Modelling in Python n = x.shape[0] self. ys = numpy.zeros([n, 4]) self. ys[2] = f.moments(4, x[2]) # cubic for j in range(2, n-2): self. ys[j+1] = f.moments(4, x[j+1]) # cubic def rollback (self, t, T, xt, xT, xtT, yT, regridder, integrator): if len(xt.shape) <> len(xT.shape) or \ len(xT.shape) <> len(yT.shape) or \ len(xt.shape) <> 1 or len(xtT.shape) <> 1: raise RuntimeError, ’expected one dimensional arrays’ nt = xt.shape[0] nT = xT.shape[0] ntT = xtT.shape[0] if nt <> nT or ntT <> nT: raise RuntimeError, ’expected array to be of same size’ if yT.shape[0] <> nT: raise RuntimeError, \ ‘array yT has different number of points to xT’ yt = numpy.zeros(nt) cT = piecewise cubic fit(xT, yT) for i in range(nt): # regrid regrid xT = numpy.zeros(nT) xti = xt[i] for j in range(nT): regrid xT[j] = xti+xtT[j] regrid yT = regridder(xT, cT, regrid xT) # polynomial fit cs = piecewise cubic fit(xtT, regrid yT) # perform expectation sum = 0 xl = xtT[2] for j in range(2, nT-2): # somehow this should be enscapsulated xh = xtT[j+1] sum = sum + integrator(cs[:, j-2], xl, xh, self. ys[j], self. ys[j+1]) xl = xh yt[i] = sum if t == 0.0: for j in range(1, nt): yt[j] = yt[0] break return yt Basic Mathematical Tools 59 def rollback(self, t, T, xt, xT, xtT, ftT, yT): # create cache of moments self. create cached moments(xtT, ftT) return self. rollback (t, T, xt, xT, xtT, yT, ftT.regrid, ftT.integral) def rollback max(self, t, T, xt, xT, xtT, ftT, yT): # create cache of moments self. create cached moments(xtT, ftT) return self. rollback (t, T, xt, xT, xtT, yT, ftT.regrid, ftT.integral max) Note that we precompute the moments in the function create cached moments() prior to performing the rollback.

Indeed Boost.Python offers many more features to help the C++ programmer to seamlessly expose C++ classes to Python and embed Python into C++. 218 Financial Modelling in Python Note that, as expected, the stochastic discount factor is a Q-martingale, in fact it is an exponential martingale, whereas the zero coupon bond price is not a Q-martingale because, as can be seen below, its SDE has a non-zero drift. d P(t, T ) = P(t, T ) (r (t)dt + (φ(t) − φ(T )) C(t)dW (t)) . (C.11) For non path-dependent pricing problems it is normally convenient to work in the so-called forward QT -measure. In this measure the numeraire at time t is simply P(t, T) and Girsanov’s theorem implies that W̄ (t), as define below, is a QT -Brownian motion d W̄ (t) = dW (t) + (φ(T ) − φ(t)) C(t)dt. Substitution of equation (C.12) into equation (C.10) yields t P(t, T ) P(0, T ) C(s)d W̄ (s) = exp − φ(T ) − φ(T ) P(t, T ) P(0, T ) 0 2 t 1 − φ(T ) − φ(T ) C(s)2 ds , ∀t ≤ T ≤ T. 2 0 (C.12) (C.13) In other words, the numeraire-rebased zero coupon bond in the forward QT -measure is a QT martingale. This to be expected in complete markets, where all numeraire-rebased tradables are martingales.


pages: 416 words: 39,022

Asset and Risk Management: Risk Oriented Finance by Louis Esch, Robert Kieffer, Thierry Lopez

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asset allocation, Brownian motion, business continuity plan, business process, capital asset pricing model, computer age, corporate governance, discrete time, diversified portfolio, implied volatility, index fund, interest rate derivative, iterative process, P = NP, p-value, random walk, risk/return, shareholder value, statistical model, stochastic process, transaction costs, value at risk, Wiener process, yield curve, zero-coupon bond

In financial modelling, several specific cases of Itô process are used, and a geometric Brownian motion is therefore obtained when: at (Xt ) = a · Xt bt (Xt ) = b · Xt An Ornstein–Uhlenbeck process corresponds to: at (Xt ) = a · (c − Xt ) bt (Xt ) = b and the square root process is such that: √ bt (Xt ) = b Xt at (Xt ) = a · (c − Xt ) 2.3.3 Stochastic differential equations Expressions of the type dXt = at (Xt ) · dt + bt (Xt ) · dwt cannot simply be handled in the same way as the corresponding determinist expressions, because wt cannot be derived. It is, however, possible to extend the definition to a concept of stochastic differential, through the theory of stochastic integral calculus.8 As the stochastic process zt is defined within the interval [a; b], the stochastic integral of zt is defined within [a; b] with respect to the standard Brownian motion wt by: a 7 8 b zt dwt = lim n→∞ δ→0 n−1 ztk (wtk+1 − wtk ) k=0 The root function presents a vertical tangent at the origin.

We no longer have a stationary random model, such as Sharpe’s example, but a model that combines the random and temporal elements; this is known as a stochastic process. An example of this type of model is the Black–Scholes model for equity options (see Section 5.3.2), where the price p is a function of various variables (price of underlying asset, realisation price, maturity, volatility of underlying asset, risk-free interest rate). In this model, the price of the underlying asset is itself modelled by a stochastic process (standard Brownian motion). 3 Equities 3.1 THE BASICS An equity is a financial asset that corresponds to part of the ownership of a company, its value being indicative of the health of the company in question. It may be the subject of a sale and purchase, either by private agreement or on an organised market. The law of supply and demand on this market determines the price of the equity. The equity can also give rise to the periodic payment of dividends. 3.1.1 Return and risk 3.1.1.1 Return on an equity Let us consider an equity over a period of time [t − 1; t] the duration of which may be one day, one week, one month or one year.

Note that this property is a generalisation for the random case of the determinist formula St = S0 · (1 + i)t . 3.4.2.2 Continuous model The method of equity value change shown in the binomial model is of the random walk type. At each transition, two movements are possible (rise or fall) with unchanged probability. When the period between each transaction tends towards 0, this type of random sequence converges towards a standard Brownian motion or SBM.52 Remember that we are looking at a stochastic process wt (a random variable that is a function of time), which obeys the following processes: • w0 = 0. • wt is a process with independent increments : if s < t < u, then wu − wt is independent of wt − ws . • wt is a process with stationary increments : the random variables wt+h − wt and wh are identically distributed. • Regardless of what t may be, the random variable √ wt is distributed according to a normal law of zero mean and standard deviation t: fwt (x) = √ 1 2πt e−x 2 /2t The first use of this process for modelling the development in the value of a financial asset was produced by L.


pages: 285 words: 78,180

Life at the Speed of Light: From the Double Helix to the Dawn of Digital Life by J. Craig Venter

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Albert Einstein, Alfred Russel Wallace, Barry Marshall: ulcers, bioinformatics, borderless world, Brownian motion, clean water, discovery of DNA, double helix, epigenetics, experimental subject, Isaac Newton, Islamic Golden Age, John von Neumann, Louis Pasteur, Mars Rover, Mikhail Gorbachev, phenotype, Richard Feynman, Richard Feynman, stem cell, the scientific method, Thomas Kuhn: the structure of scientific revolutions, Turing machine

Einstein’s notion was eventually confirmed with careful experiments conducted in Paris by Jean Baptiste Perrin (1870–1942), who was rewarded for this and other work with the Nobel Prize in Physics in 1926. Brownian motion has profound consequences when it comes to understanding the workings of living cells. Many of the vital components of a cell, such as DNA, are larger than individual atoms but still small enough to be jostled by the constant pounding of the surrounding sea of atoms and molecules. So while DNA is indeed shaped like a double helix, it is a writhing, twisting, spinning helix as a result of the forces of random Brownian motion. The protein robots of living cells are only able to fold into their proper shapes because their components are mobile chains, sheets, and helices that are constantly buffeted within the cell’s protective membrane. Life is driven by Brownian motion, from the kinesin protein trucks that pull tiny sacks of chemicals along microtubules to the spinning ATP synthase.31 Critically, the amount of Brownian motion depends on temperature: too low and there is not enough motion; too high and all structures become randomized by the violent motion.

Life is driven by Brownian motion, from the kinesin protein trucks that pull tiny sacks of chemicals along microtubules to the spinning ATP synthase.31 Critically, the amount of Brownian motion depends on temperature: too low and there is not enough motion; too high and all structures become randomized by the violent motion. Thus life can only exist in a narrow temperature range. Within this range, the equivalent of a Richter 9 earthquake rages continuously inside cells. “You would not need to even pedal your bicycle: you would simply attach a ratchet to the wheel preventing it from going backwards and shake yourselves forward,” according to George Oster and Hongyun Wang, of the Department of Molecular and Cellular Biology at the University of California, Berkeley.32 Protein robots accomplish a comparable feat by using ratchets and power strokes to harness the power of Brownian motion. Due to the incessant random movement and vibrations of molecules, diffusion is very rapid over short distances, which enables biological reactions to occur with tiny quantities of reactants in the extremely confined volumes of most cells.

A protein with one hundred amino acids can fold in myriad ways, such that the number of alternate structures ranges from 2100 to 10100 possible conformations. For each protein to try every possible conformation would require on the order of ten billion years. But built into the linear protein code are the folding instructions, which are in turn determined by the linear genetic code. As a result, with the help of Brownian motion, the incessant molecular movement caused by heat energy, these processes happen very quickly—in a few thousandths of a second. They are driven by the fact that a correctly folded protein has the lowest possible free energy, so that, like water flowing to the lowest point, the protein naturally achieves its favored shape. The correctly folded conformation that ensures that the enzyme can work properly involves moving from a high degree of entropy and free energy to the thermodynamically stable state of decreased entropy and free energy.


pages: 461 words: 128,421

The Myth of the Rational Market: A History of Risk, Reward, and Delusion on Wall Street by Justin Fox

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Albert Einstein, Andrei Shleifer, asset allocation, asset-backed security, bank run, Benoit Mandelbrot, Black-Scholes formula, Bretton Woods, Brownian motion, capital asset pricing model, card file, Cass Sunstein, collateralized debt obligation, complexity theory, corporate governance, Credit Default Swap, credit default swaps / collateralized debt obligations, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, discovery of the americas, diversification, diversified portfolio, Edward Glaeser, endowment effect, Eugene Fama: efficient market hypothesis, experimental economics, financial innovation, Financial Instability Hypothesis, floating exchange rates, George Akerlof, Henri Poincaré, Hyman Minsky, implied volatility, impulse control, index arbitrage, index card, index fund, invisible hand, Isaac Newton, John Nash: game theory, John von Neumann, joint-stock company, Joseph Schumpeter, libertarian paternalism, linear programming, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, market bubble, market design, New Journalism, Nikolai Kondratiev, Paul Lévy, pension reform, performance metric, Ponzi scheme, prediction markets, pushing on a string, quantitative trading / quantitative finance, Ralph Nader, RAND corporation, random walk, Richard Thaler, risk/return, road to serfdom, Robert Shiller, Robert Shiller, rolodex, Ronald Reagan, shareholder value, Sharpe ratio, short selling, side project, Silicon Valley, South Sea Bubble, statistical model, The Chicago School, The Myth of the Rational Market, The Predators' Ball, the scientific method, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Kuhn: the structure of scientific revolutions, Thomas L Friedman, Thorstein Veblen, Tobin tax, transaction costs, tulip mania, value at risk, Vanguard fund, volatility smile, Yogi Berra

Another famous example came in the mid-1920s when the young founder of Moscow’s Business Cycle Institute, Nikolai Kondratiev, proposed that economic activity moved in half-century-long “waves.”35 As the study of statistics progressed and the mathematics of random processes such as Brownian motion became more widely understood, those on the frontier of this work began to question these apparent cycles. In his November 1925 presidential address to Great Britain’s Royal Statistical Society, Cambridge professor George Udny Yule demonstrated that random Brownian motion could, with a little tweaking, produce dramatic patterns that didn’t look random at all.36 A few years later, a mathematician working for Kondratiev in Moscow penned what came to be seen as the definitive debunking of the pattern finders. “Almost all of the phenomena of economic life,” wrote Eugen Slutsky, “occur in sequences of rising and falling movements, like waves.”

The mathematical expectation of the speculator was the expected return of the stock or of the overall market, around which the actual return would fluctuate randomly. It is conceivable that Bachelier and Poincaré were aware of these flaws in 1900, and didn’t bother correcting them because Bachelier’s formula was meant to look only an “instant” into the future. It didn’t matter that Bachelier’s Brownian motion would eventually lead prices where they could not go, because he had made explicit that it was not to be used for purposes of long-term prediction anyway. Beset by no such qualms, Samuelson revised Bachelier’s formula. He introduced what he variously called “geometric,” “economic,” or “logarithmic” Brownian motion, which avoided negative prices by describing percentage moves of stock prices, not dollars and cents. And he depicted stock market investing as a bet in which the payoffs fluctuated randomly around the expected return. SAMUELSON BEGAN TALKING UP THESE ideas around MIT and in visits to other universities in the late 1950s.

After some study of the market, he concluded: It was a game of competitive gambling. In it some were smart and some were not so smart, and the players changed sides so often that it was a picture of financial chaos or bedlam. As I had some experience in molecular chaos as a physicist studying statistical mechanics, the analogies were very clear to me indeed.7 The analogy that was clearest to him was that of Brownian motion. As Samuelson had already noticed, straight arithmetic Brownian motion couldn’t possibly fit the data. Instead, Osborne used the same percentage-change version as Samuelson had, then published his findings in the March–April 1959 issue of the journal Operations Research. As soon as the article came out, letters pointing out similarities to the stock market work of Bachelier, Maurice Kendall, and others came pouring in. Osborne hadn’t known about any of that beforehand.


pages: 425 words: 122,223

Capital Ideas: The Improbable Origins of Modern Wall Street by Peter L. Bernstein

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Albert Einstein, asset allocation, backtesting, Benoit Mandelbrot, Black-Scholes formula, Bonfire of the Vanities, Brownian motion, buy low sell high, capital asset pricing model, debt deflation, diversified portfolio, Eugene Fama: efficient market hypothesis, financial innovation, financial intermediation, fixed income, full employment, implied volatility, index arbitrage, index fund, interest rate swap, invisible hand, John von Neumann, Joseph Schumpeter, law of one price, linear programming, Louis Bachelier, mandelbrot fractal, martingale, means of production, new economy, New Journalism, profit maximization, Ralph Nader, RAND corporation, random walk, Richard Thaler, risk/return, Robert Shiller, Robert Shiller, Ronald Reagan, stochastic process, the market place, The Predators' Ball, the scientific method, The Wealth of Nations by Adam Smith, Thorstein Veblen, transaction costs, transfer pricing, zero-coupon bond

If stock prices vary according to the square root of time, they bear a remarkable resemblance to molecules randomly colliding with one another as they move in space. An English physicist named Robert Brown discovered this phenomenon early in the nineteenth century, and it is generally known as Brownian motion. Brownian motion was a critical ingredient of Einstein’s theory of the atom. The mathematical formula that describes this phenomenon was one of Bachelier’s crowning achievements. Over time, in the literature on finance, Brownian motion came to be called the random walk, which someone once described as the path a drunk might follow at night in the light of a lamppost. No one knows who first used this expression, but it became increasingly familiar among academics during the 1960s, much to the annoyance of financial practitioners.

Second, again unaware that he was echoing Bachelier, Osborne argues that prices represent decisions at those moments—and only at those moments—when the buyer expects a stock to rise in price and the seller expects it to fall: Transactions take place only when there is a difference of opinion. This means that, for the market as a whole, the expected price change is zero. The market is as likely to go up x percent as down x percent. Third, Osborne’s mathematical manipulations show that the range within which prices tend to fluctuate will “increase as the square root of the time interval”26—Brownian motion, precisely as Bachelier had prophesied. Fourth, in a set of experiments with actual stock market data, Osborne confirms the hypothesis of Brownian motion, including percentage price changes over intervals of a day, a week, a month, two months, up to twelve years. He also finds that Cowles’s long history of stock prices follows “. . . the square root of time diffusion law very nicely indeed.”27 Finally, he finds that distributions of the monthly changes in the Dow Jones Industrial Average from 1925 to 1956 “are quite comparable.”28 The fifth finding made by Osborne’s imaginary statistician is another example of how Osborne, working all by himself, confirmed the research conclusions of others.

See also Wells Fargo Bank Barr Rosenberg Associates (BARRA) Battle for Investment Survival, The (Loeb) “Behavior of Stock Prices, The” (Fama) Bell Journal Bell Laboratories Beta: see Risk, systematic “Beta Revolution: Learning to Live with Risk” Black Monday (October, 1987, crash) Black/Scholes formula Block trading Boeing Bond(s) convertible discount rates and government high-grade interest rates international junk liquidity maturity risk treasury: see Bond(s), government zero-coupon Bond market Boston Company Brokerage commissions. See also Transaction costs Brownian motionBrownian Motion in the Stock Market” (Osborne) Butterfly swaps Buy and hold strategy California Public Employees Retirement System Calls: see Options Capital cost of optimal structure of preserving strategy “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk” (Sharpe) Capital Asset Pricing Model (CAPM) non-stock applicability risk/return ratio in time analysis and Capital gains tax Capital Guardian Capital markets theory competition and corporate investment and debt/equity ratios and research CAPM: see Capital Asset Pricing Model CDs CEIR Center for Research in Security Prices (CRSP).

Mathematical Finance: Core Theory, Problems and Statistical Algorithms by Nikolai Dokuchaev

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Black-Scholes formula, Brownian motion, buy low sell high, discrete time, fixed income, implied volatility, incomplete markets, martingale, random walk, short selling, stochastic process, stochastic volatility, transaction costs, volatility smile, Wiener process, zero-coupon bond

The initial price S0>0 is a given non-random value, and the evolution of S(t) is described by the following Ito equation: dS(t)=S(t)(a(t)dt+σ(t)dw(t)). (5.1) Here w(t) is a (one-dimensional) Wiener process, and a and σ are market parameters. Sometimes in the literature S(t) is called a geometric Brownian motion (for the case of non-random and constant a, σ), sometimes ln S(t) is also said to be a Brownian motion. Mathematicians prefer to use the term ‘Brownian motion’ for w(t) only (i.e., Brownian motion is the same as a Wiener process). Definition 5.1 In (5.1), a(t) is said to be the appreciation rate, σ(t) is said to be the volatility. Note that, in terms of more general stochastic differential equations, the coefficient for dt (i.e., a(t)S(t)) is said to be the drift (or the drift coefficient), and the coefficient for dw(t) (i.e., σ(t)S(t)) is said to be the diffusion coefficient.

Prove that there exists an American option (Definition 3.43) such that its fair price is equal to the fair price of the option from Problem 3.44. © 2007 Nikolai Dokuchaev 4 Basics of Ito calculus and stochastic analysis This chapter introduces the stochastic integral, stochastic differential equations, and core results of Ito calculus. 4.1 Wiener process (Brownian motion) Let T>0 be given, Definition 4.1 We say that a continuous time random process w(t) is a (onedimensional) Wiener process (or Brownian motion) if (i) w(0)=0; (ii) w(t) is Gaussian with Ew(t)=0, Ew(t)2=t, i.e., w(t) is distributed as N(0, t); (iii) w(t+τ)−w(t) does not depend on {w(s), s≤t} for all t≥0, τ>0. Theorem 4.2 (N. Wiener). There exists a probability space such that there exists a pathwise continuous process with these properties. This is why we call it the Wiener process.


pages: 695 words: 194,693

Money Changes Everything: How Finance Made Civilization Possible by William N. Goetzmann

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Albert Einstein, Andrei Shleifer, asset allocation, asset-backed security, banking crisis, Benoit Mandelbrot, Black Swan, Black-Scholes formula, Bretton Woods, Brownian motion, capital asset pricing model, Cass Sunstein, collective bargaining, colonial exploitation, compound rate of return, conceptual framework, corporate governance, Credit Default Swap, David Ricardo: comparative advantage, debt deflation, delayed gratification, Detroit bankruptcy, disintermediation, diversified portfolio, double entry bookkeeping, Edmond Halley, en.wikipedia.org, equity premium, financial independence, financial innovation, financial intermediation, fixed income, frictionless, frictionless market, full employment, high net worth, income inequality, index fund, invention of the steam engine, invention of writing, invisible hand, James Watt: steam engine, joint-stock company, joint-stock limited liability company, laissez-faire capitalism, Louis Bachelier, mandelbrot fractal, market bubble, means of production, money: store of value / unit of account / medium of exchange, moral hazard, new economy, passive investing, Paul Lévy, Ponzi scheme, price stability, principal–agent problem, profit maximization, profit motive, quantitative trading / quantitative finance, random walk, Richard Thaler, Robert Shiller, Robert Shiller, shareholder value, short selling, South Sea Bubble, sovereign wealth fund, spice trade, stochastic process, the scientific method, The Wealth of Nations by Adam Smith, Thomas Malthus, time value of money, too big to fail, trade liberalization, trade route, transatlantic slave trade, transatlantic slave trade, tulip mania, wage slave

It also required the time period for which the option is granted (the “maturity” of the option). Bachelier presented his book, Théorie de la Spéculation, as his doctoral thesis in mathematics at the Sorbonne in 1900. In working through the problem of option pricing, Bachelier had to devise a precise definition of how a stock price moved randomly through time. We now refer to this as Brownian motion. Interestingly, Albert Einstein developed a Brownian motion model in 1905, evidently later and independently from Bachelier. Bachelier’s answer to the option pricing problem turned out to be an equation beyond the knowledge of market participants at the time. This presented an interesting philosophical issue. If option prices conformed to a complex, nonlinear multivariate function that was undiscovered until 1900, how then did the invisible hand—the process of speculation—drive them toward efficiency?

Evidently none knew of Bachelier, and thus they had to retrace the mathematical logic of fair prices and random walks when they began work on the problem of option pricing in the late 1960s. Like Bachelier, they relied on a model of variation in prices—Brownian motion—although unlike Bachelier, they chose one that did not allow prices to become negative—a limitation of Bachelier’s work. The Black-Scholes formula, as it is now referred to, was mathematically sophisticated, but at its heart it contained a novel economic—as opposed to mathematical—insight. They discovered that the invisible hand setting option prices was risk-neutral. Option payoffs could be replicated risklessly, provided one could trade in an ideal, frictionless market in which stocks behaved according to Brownian motion. Later researchers4 developed a simple framework called a “binomial model” that was able to match the payoff of a put or a call by trading just the stock and a bond through time.

Paul Lévy formalized these prior random walk models into a very general family of stochastic processes referred to as Lévy processes. Brownian motion was just one process in the family of Lévy processes—and perhaps the best behaved of them. Other stochastic processes have such things as discontinuous jumps and unusually large shocks (which might, for example, explain the crash of 1987, when the US stock market lost 22.6% of its value in a single day). In the 1960s, Benoit Mandelbrot began to investigate whether Lévy processes described economic time series like cotton prices and stock prices. He found that the ones that generated jumps and extreme events better described financial markets. He developed a mathematics around these unusual Lévy processes that he called “fractal geometry.” He argued that unusual events—Taleb’s black swan—were in fact much more common phenomena than Brownian motion would suggest.


pages: 266 words: 86,324

The Drunkard's Walk: How Randomness Rules Our Lives by Leonard Mlodinow

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Albert Einstein, Alfred Russel Wallace, Antoine Gombaud: Chevalier de Méré, Atul Gawande, Brownian motion, butterfly effect, correlation coefficient, Daniel Kahneman / Amos Tversky, Donald Trump, feminist movement, forensic accounting, Gerolamo Cardano, Henri Poincaré, index fund, Isaac Newton, law of one price, pattern recognition, Paul Erdős, probability theory / Blaise Pascal / Pierre de Fermat, RAND corporation, random walk, Richard Feynman, Richard Feynman, Ronald Reagan, Stephen Hawking, Steve Jobs, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, V2 rocket, Watson beat the top human players on Jeopardy!

Then, in a deathblow to his wishful interpretation of the discovery, Brown also observed the motion when looking at inorganic particles—of asbestos, copper, bismuth, antimony, and manganese. He knew then that the movement he was observing was unrelated to the issue of life. The true cause of Brownian motion would prove to be the same force that compelled the regularities in human behavior that Quételet had noted—not a physical force but an apparent force arising from the patterns of randomness. Unfortunately, Brown did not live to see this explanation of the phenomenon he observed. The groundwork for the understanding of Brownian motion was laid in the decades that followed Brown’s work, by Boltzmann, Maxwell, and others. Inspired by Quételet, they created the new field of statistical physics, employing the mathematical edifice of probability and statistics to explain how the properties of fluids arise from the movement of the (then hypothetical) atoms that make them up.

But actually it did take an Einstein to finally convince the scientific world of the need for that new approach to physics. Albert Einstein did it in 1905, the same year in which he published his first work on relativity. And though hardly known in popular culture, Einstein’s 1905 paper on statistical physics proved equally revolutionary. In the scientific literature, in fact, it would become his most cited work.32 EINSTEIN’S 1905 WORK on statistical physics was aimed at explaining a phenomenon called Brownian motion. The process was named for Robert Brown, botanist, world expert in microscopy, and the person credited with writing the first clear description of the cell nucleus. Brown’s goal in life, pursued with relentless energy, was to discover through his observations the source of the life force, a mysterious influence believed in his day to endow something with the property of being alive. In that quest, Brown was doomed to failure, but one day in June 1827, he thought he had succeeded.

But most physicists are practical, and so the most important roadblock to acceptance was that although the theory reproduced some laws that were known, it made few new predictions. And so matters stood until 1905, when long after Maxwell was dead and shortly before a despondent Boltzmann would commit suicide, Einstein employed the nascent theory to explain in great numerical detail the precise mechanism of Brownian motion.34 The necessity of a statistical approach to physics would never again be in doubt, and the idea that matter is made of atoms and molecules would prove to be the basis of most modern technology and one of the most important ideas in the history of physics. The random motion of molecules in a fluid can be viewed, as we’ll note in chapter 10, as a metaphor for our own paths through life, and so it is worthwhile to take a little time to give Einstein’s work a closer look.


pages: 282 words: 89,436

Einstein's Dice and Schrödinger's Cat: How Two Great Minds Battled Quantum Randomness to Create a Unified Theory of Physics by Paul Halpern

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Albert Einstein, Albert Michelson, Arthur Eddington, Brownian motion, clockwork universe, cosmological constant, dark matter, double helix, Ernest Rutherford, Fellow of the Royal Society, Isaac Newton, John von Neumann, lone genius, Murray Gell-Mann, New Journalism, Richard Feynman, Richard Feynman, Schrödinger's Cat, Solar eclipse in 1919, The Present Situation in Quantum Mechanics

But that result was just the overture of his grand symphony of scientific revelations. Another major paper Einstein published in 1905 concerned a phenomenon called Brownian motion, named after the Scottish botanist Robert Brown, involving tiny random fluctuations of small particles. In 1827, Brown had observed the agitated motion of particles found in pollen grains immersed in water. He failed to find a credible explanation for their erratic behavior. Building upon his doctoral thesis, Einstein decided to model the movements of particles bashed around by water molecules and discovered precisely the kind of haphazard jig seen by Brown. By explaining Brownian motion as the zigzag result of 35 Einstein’s Dice and Schrödinger’s Cat myriad particle collisions, Einstein furnished important evidence for the existence of atoms.

Nothing in this practical work would hint at the explosion of ideas about to be ignited. In the spring of that year, Einstein took aim. Staring classical physics straight in the face, he lit the fuses and launched his grenades. He submitted four papers to a prestigious journal, Annalen der Physik. One was a version of his dissertation. The other three articles— addressing the photoelectric effect, Brownian motion, and the special theory of relativity—would shake the foundations of physical science. Einstein’s paper on the photoelectric effect cemented Planck’s quantum idea by making it tangible and eminently measurable. It considers what would happen if a researcher shines a light on a metal, supplying enough energy to release an electron. If light were purely a wave, theory suggested, its amount of energy would depend mainly on its 34 The Clockwork Universe brightness.

(Schrödinger), 208 Aristotle, 77, 215 Arkani-Hamed, Nima, 232 Ashtekar, Abhay, 232 Aspect, Alain, 210 Assembly of German Natural Scientists and Physicians (Vienna conference of 1913), 44–51 Atomic bomb Einstein and, 168–169, 183 Germany’s efforts to develop, 178–180 Atomic model, 35 Bohr, 46–48, 73, 81, 82, 84–85 Bohr-Sommerfeld, 83, 98 Rutherford, 45 Atomism, 28, 80 Atoms argument over reality of, 22–24 photoelectric effect and, 35 as probabilistic mechanism, 102 Autiero, Dario, 235 Axioms, 18 Aydelotte, Frank, 168 Bailey, Herbert, 204, 205 Ball-in-the-box thought experiment, 139, 141 Balmer series, 48 Bär, Richard, 154, 155 Bargmann, Sonja, 204 Bargmann, Valentine “Valya,” 149, 168, 169 Barnett, Lincoln, 204 Bauer, Alexander, 16 Bauer, Minnie, 16 Bauer-Bohm, Hansi, 143–144 Becquerel, Henri, 28 Bell, John, 210 Berg, Moe, 179 255 Index Heisenberg and, 86–87, 88 probabilistic interpretation and, 105 Schrödinger wave equation and, 5, 6 wavefunction as ghost field and, 99–100 Bose, Satyendra, 90, 92, 225 Bose-Einstein statistics, 90 Bosonic strings, 230–231 Bosons, 225–227, 230 Bottom quarks, 227 Braunizer, Andreas, 217 Braunizer, Arnulf, 217 Braunizer, Ruth, 219–220 Brecht, Bertolt, 109 Brout, Robert, 226 Brown, Robert, 35 Brownian motion, Einstein on, 34, 35–36 Buddhism/Buddha, 77, 80 Bergmann, Peter, 149, 168, 169, 213, 231 Berlin, 109, 131 Bertel, Annemarie “Anny,” 76, 77 Bertolucci, Sergio, 235 Besso, Michele, 29, 55–56 Beta decay, 136 “Big Bang,” 63 Birch, Francis, 192 BKS (Bohr-Kramers-Slater) theory, 103 Blackbody radiation, 31–32, 90 Black holes, 59 Black Mountain College, 169 Bohm, David, 209–210 Bohm-Aharonov version of EPR thought experiment, 209–210 Bohr, Margrethe, 102 Bohr, Niels, 1, 110, 215 atomic model, 35, 46–48, 73, 81, 82, 84–85 Eddington’s theory and, 148 Einstein and, 137, 168, 200 EPR paper and, 138 escape from Denmark, 179 uncertainty principle and, 106 “Bohr Festival,” 82, 84–85 Bohr’s Institute for Theoretical Physics, 88, 100–102 Bohr-Sommerfeld atomic model, 83, 98 Bohr-Sommerfeld quantization rules, 93 Boltzmann, Ludwig, 22–23, 24, 30, 81, 92 Bondi, Hermann, 157 Borges, Jorge Luis, 62 Born, Max, 1, 82, 87, 89, 144 dismissal and exile of, 128, 130 Einstein and, 103–104, 134 as go-between in de Valera offer to Schrödinger, 154, 155 Calabi, Eugenio, 231 Calabi-Yau manifolds, 231 Callaway, Joseph, 208 Caltech, Einstein’s visits to, 122–123 “Can Quantum Mechanical Description of Physical Reality Be Considered Complete?”

Mathematics for Finance: An Introduction to Financial Engineering by Marek Capinski, Tomasz Zastawniak

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Black-Scholes formula, Brownian motion, capital asset pricing model, cellular automata, delta neutral, discounted cash flows, discrete time, diversified portfolio, interest rate derivative, interest rate swap, locking in a profit, London Interbank Offered Rate, margin call, martingale, quantitative trading / quantitative finance, random walk, short selling, stochastic process, time value of money, transaction costs, value at risk, Wiener process, zero-coupon bond

N tN As N → ∞, we have tN → t and N tN → ∞, so that wN (tN ) → W (t) √ in distribution, where W (t) = tX. The last equality means that W (t) is normally distributed with mean 0 and variance t. This argument, based on the Central Limit Theorem, works for any single fixed time t > 0. It is possible to extend the result to obtain a limit for all times t ≥ 0 simultaneously, but this is beyond the scope of this book. The limit W (t) is called the Wiener process (or Brownian motion). It inherits many of the properties of the random walk, for example: 1. W (0) = 0, which corresponds to wN (0) = 0. 2. E(W (t)) = 0, corresponding to E(wN (t)) = 0 (see the solution of Exercise 3.25). 3. Var(W (t)) = t, with the discrete counterpart Var(wN (t)) = t (see the solution of Exercise 3.25). 4. The increments W (t3 ) − W (t2 ) and W (t2 ) − W (t1 ) are independent for 0 ≤ t1 ≤ t2 ≤ t3 ; so are the increments wN (t3 ) − wN (t2 ) and wN (t2 ) − wN (t1 ). 2 See, for example, Capiński and Zastawniak (2001). 70 Mathematics for Finance 5.

Our treatment of continuous time is a compromise lacking full mathematical rigour, which would require a systematic study of Stochastic Calculus, a topic 186 Mathematics for Finance treated in detail in more advanced texts. In place of this, we shall exploit an analogy with the discrete time case. As a starting point we take the continuous time model of stock prices developed in Chapter 3 as a limit of suitably scaled binomial models with time steps going to zero. In the resulting continuous time model the stock price is given by (8.5) S(t) = S(0)emt+σW (t) , where W (t) is the standard Wiener process (Brownian motion), see Section 3.3.2. This means, in particular, that S(t) has the log normal distribution. Consider a European option on the stock expiring at time T with payoff f (S(T )). As in the discrete-time case, see Theorem 8.4, the time 0 price D(0) of the option ought to be equal to the expectation of the discounted payoff e−rT f (S(T )), (8.6) D(0) = E∗ e−rT f (S(T )) , under a risk-neutral probability P∗ that turns the discounted stock price process e−rt S(t) into a martingale.

Glossary of Symbols A B β c C C CA CE E C Cov delta div div0 D D DA E E∗ f F gamma Φ k K i m fixed income (risk free) security price; money market account bond price beta factor covariance call price; coupon value covariance matrix American call price European call price discounted European call price covariance Greek parameter delta dividend present value of dividends derivative security price; duration discounted derivative security price price of an American type derivative security expectation risk-neutral expectation futures price; payoff of an option; forward rate forward price; future value; face value Greek parameter gamma cumulative binomial distribution logarithmic return return coupon rate compounding frequency; expected logarithmic return 305 306 Mathematics for Finance M m µ N N k ω Ω p p∗ P PA PE P E PA r rdiv re rF rho ρ S S σ t T τ theta u V Var VaR vega w w W x X y z market portfolio expected returns as a row matrix expected return cumulative normal distribution the number of k-element combinations out of N elements scenario probability space branching probability in a binomial tree risk-neutral probability put price; principal American put price European put price discounted European put price present value factor of an annuity interest rate dividend yield effective rate risk-free return Greek parameter rho correlation risky security (stock) price discounted risky security (stock) price standard deviation; risk; volatility current time maturity time; expiry time; exercise time; delivery time time step Greek parameter theta row matrix with all entries 1 portfolio value; forward contract value, futures contract value variance value at risk Greek parameter vega symmetric random walk; weights in a portfolio weights in a portfolio as a row matrix Wiener process, Brownian motion position in a risky security strike price position in a fixed income (risk free) security; yield of a bond position in a derivative security Index admissible – portfolio 5 – strategy 79, 88 American – call option 147 – derivative security – put option 147 amortised loan 30 annuity 29 arbitrage 7 at the money 169 attainable – portfolio 107 – set 107 183 basis – of a forward contract 128 – of a futures contract 140 basis point 218 bear spread 208 beta factor 121 binomial – distribution 57, 180 – tree model 7, 55, 81, 174, 238 Black–Derman–Toy model 260 Black–Scholes – equation 198 – formula 188 bond – at par 42, 249 – callable 255 – face value 39 – fixed-coupon 255 – floating-coupon 255 – maturity date 39 – stripped 230 – unit 39 – with coupons 41 – zero-coupon 39 Brownian motion 69 bull spread 208 butterfly 208 – reversed 209 call option 13, 181 – American 147 – European 147, 188 callable bond 255 cap 258 Capital Asset Pricing Model 118 capital market line 118 caplet 258 CAPM 118 Central Limit Theorem 70 characteristic line 120 compounding – continuous 32 – discrete 25 – equivalent 36 – periodic 25 – preferable 36 conditional expectation 62 contingent claim 18, 85, 148 – American 183 – European 173 continuous compounding 32 continuous time limit 66 correlation coefficient 99 coupon bond 41 coupon rate 249 307 308 covariance matrix 107 Cox–Ingersoll–Ross model 260 Cox–Ross–Rubinstein formula 181 cum-dividend price 292 delta 174, 192, 193, 197 delta hedging 192 delta neutral portfolio 192 delta-gamma hedging 199 delta-gamma neutral portfolio 198 delta-vega hedging 200 delta-vega neutral portfolio 198 derivative security 18, 85, 253 – American 183 – European 173 discount factor 24, 27, 33 discounted stock price 63 discounted value 24, 27 discrete compounding 25 distribution – binomial 57, 180 – log normal 71, 186 – normal 70, 186 diversifiable risk 122 dividend yield 131 divisibility 4, 74, 76, 87 duration 222 dynamic hedging 226 effective rate 36 efficient – frontier 115 – portfolio 115 equivalent compounding 36 European – call option 147, 181, 188 – derivative security 173 – put option 147, 181, 189 ex-coupon price 248 ex-dividend price 292 exercise – price 13, 147 – time 13, 147 expected return 10, 53, 97, 108 expiry time 147 face value 39 fixed interest 255 fixed-coupon bond 255 flat term structure 229 floating interest 255 floating-coupon bond 255 floor 259 floorlet 259 Mathematics for Finance forward – contract 11, 125 – price 11, 125 – rate 233 fundamental theorem of asset pricing 83, 88 future value 22, 25 futures – contract 134 – price 134 gamma 197 Girsanov theorem 187 Greek parameters 197 growth factor 22, 25, 32 Heath–Jarrow–Morton model hedging – delta 192 – delta-gamma 199 – delta-vega 200 – dynamic 226 in the money 169 initial – forward rate 232 – margin 135 – term structure 229 instantaneous forward rate interest – compounded 25, 32 – fixed 255 – floating 255 – simple 22 – variable 255 interest rate 22 interest rate option 254 interest rate swap 255 261 233 LIBID 232 LIBOR 232 line of best fit 120 liquidity 4, 74, 77, 87 log normal distribution 71, 186 logarithmic return 34, 52 long forward position 11, 125 maintenance margin 135 margin call 135 market portfolio 119 market price of risk 212 marking to market 134 Markowitz bullet 113 martingale 63, 83 Index 309 martingale probability 63, 250 maturity date 39 minimum variance – line 109 – portfolio 108 money market 43, 235 no-arbitrage principle 7, 79, 88 normal distribution 70, 186 option – American 183 – at the money 169 – call 13, 147, 181, 188 – European 173, 181 – in the money 169 – interest rate 254 – intrinsic value 169 – out of the money 169 – payoff 173 – put 18, 147, 181, 189 – time value 170 out of the money 169 par, bond trading at 42, 249 payoff 148, 173 periodic compounding 25 perpetuity 24, 30 portfolio 76, 87 – admissible 5 – attainable 107 – delta neutral 192 – delta-gamma neutral 198 – delta-vega neutral 198 – expected return 108 – market 119 – variance 108 – vega neutral 197 positive part 148 predictable strategy 77, 88 preferable compounding 36 present value 24, 27 principal 22 put option 18, 181 – American 147 – European 147, 189 put-call parity 150 – estimates 153 random interest rates random walk 67 rate – coupon 249 – effective 36 237 – forward 233 – – initial 232 – – instantaneous 233 – of interest 22 – of return 1, 49 – spot 229 regression line 120 residual random variable 121 residual variance 122 return 1, 49 – expected 53 – including dividends 50 – logarithmic 34, 52 reversed butterfly 209 rho 197 risk 10, 91 – diversifiable 122 – market price of 212 – systematic 122 – undiversifiable 122 risk premium 119, 123 risk-neutral – expectation 60, 83 – market 60 – probability 60, 83, 250 scenario 47 security market line 123 self-financing strategy 76, 88 short forward position 11, 125 short rate 235 short selling 5, 74, 77, 87 simple interest 22 spot rate 229 Standard and Poor Index 141 state 238 stochastic calculus 71, 185 stochastic differential equation 71 stock index 141 stock price 47 strategy 76, 87 – admissible 79, 88 – predictable 77, 88 – self-financing 76, 88 – value of 76, 87 strike price 13, 147 stripped bond 230 swap 256 swaption 258 systematic risk 122 term structure 229 theta 197 time value of money 21 310 trinomial tree model Mathematics for Finance 64 underlying 85, 147 undiversifiable risk 122 unit bond 39 value at risk 202 value of a portfolio 2 value of a strategy 76, 87 VaR 202 variable interest 255 Vasiček model 260 vega 197 vega neutral portfolio volatility 71 weights in a portfolio Wiener process 69 yield 216 yield to maturity 229 zero-coupon bond 39 197 94


pages: 312 words: 35,664

The Mathematics of Banking and Finance by Dennis W. Cox, Michael A. A. Cox

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barriers to entry, Brownian motion, call centre, correlation coefficient, inventory management, iterative process, linear programming, meta analysis, meta-analysis, P = NP, pattern recognition, random walk, traveling salesman, value at risk

Further, a 2 is equally likely to appear on any subsequent roll of the dice. 4.3 ESTIMATION OF PROBABILITIES There are a number of ways in which you can arrive at an estimate of Prob(A) for the event A. Three possible approaches are: r A subjective approach, or ‘guess work’, which is used when an experiment cannot be easily r repeated, even conceptually. Typical examples of this include horse racing and Brownian motion. Brownian motion represents the random motion of small particles suspended in a gas or liquid and is seen, for example, in the random walk pattern of a drunken man. The classical approach, which is usually adopted if all sample points are equally likely (as is the case in the rolling of a dice as discussed above). The probability may be measured with certainty by analysing the event. Using the same mathematical notation, a mathematical definition of this is: Prob(A) = Number of events classifiable as A Total number of possible events A typical example of such a probability is a lottery.

Index a notation 103–4, 107–20, 135–47 linear regression 103–4, 107–20 slope significance test 112–20 variance 112 abscissa see horizontal axis absolute value, notation 282–4 accuracy and reliability, data 17, 47 adaptive resonance theory 275 addition, mathematical notation 279 addition of normal variables, normal distribution 70 addition rule, probability theory 24–5 additional variables, linear programming 167–70 adjusted cash flows, concepts 228–9 adjusted discount rates, concepts 228–9 Advanced Measurement Approach (AMA) 271 advertising allocation, linear programming 154–7 air-conditioning units 182–5 algorithms, neural networks 275–6 alternatives, decisions 191–4 AMA see Advanced Measurement Approach analysis data 47–52, 129–47, 271–4 Latin squares 131–2, 143–7 linear regression 110–20 projects 190–2, 219–25, 228–34 randomised block design 129–35 sampling 47–52, 129–47 scenario analysis 40, 193–4, 271–4 trends 235–47 two-way classification 135–47 variance 110–20, 121–7 anonimised databases, scenario analysis 273–4 ANOVA (analysis of variance) concepts 110–20, 121–7, 134–47 examples 110–11, 123–7, 134–40 formal background 121–2 linear regression 110–20 randomised block design 134–5, 141–3 tables 110–11, 121–3, 134–47 two-way classification 136–7 appendix 279–84 arithmetic mean, concepts 37–45, 59–60, 65–6, 67–74, 75–81 assets classes 149–57 reliability 17, 47, 215–18, 249–60 replacement of assets 215–18, 249–60 asymptotic distributions 262 ATMs 60 averages see also mean; median; mode concepts 37–9 b notation 103–4, 107–20, 132–5 linear regression 103–4, 107–20 variance 112 back propagation, neural networks 275–7 backwards recursion 179–87 balance sheets, stock 195 bank cashier problem, Monte Carlo simulation 209–12 Bank for International Settlements (BIS) 267–9, 271 banks Basel Accord 262, 267–9, 271 failures 58 loss data 267–9, 271–4 modelling 75–81, 85, 97, 267–9, 271–4 profitable loans 159–66 bar charts comparative data 10–12 concepts 7–12, 54, 56, 59, 205–6, 232–3 discrete data 7–12 examples 9–12, 205–6, 232–3 286 Index bar charts (cont.) narrative explanations 10 relative frequencies 8–12 rules 8–9 uses 7–12, 205–6, 232–3 base rates, trends 240 Basel Accord 262, 267–9, 271 bathtub curves, reliability concepts 249–51 Bayes’theorem, probability theory 27–30, 31 bell-shaped normal distribution see normal distribution bi-directional associative memory 275 bias 1, 17, 47–50, 51–2, 97, 129–35 randomised block design 129–35 sampling 17, 47–50, 51–2, 97, 129–35 skewness 41–5 binomial distribution concepts 55–8, 61–5, 71–2, 98–9, 231–2 examples 56–8, 61–5, 71–2, 98–9 net present value (NPV) 231–2 normal distribution 71–2 Pascal’s triangle 56–7 uses 55, 57, 61–5, 71–2, 98–9, 231–2 BIS see Bank for International Settlements boards of directors 240–1 break-even analysis, concepts 229–30 Brownian motion 22 see also random walks budgets 149–57 calculators, log functions 20, 61 capital Basel Accord 262, 267–9, 271 cost of capital 219–25, 229–30 cash flows adjusted cash flows 228–9 future cash flows 219–25, 227–34, 240–1 net present value (NPV) 219–22, 228–9, 231–2 standard deviation 232–4 central limit theorem concepts 70, 75 examples 70 chi-squared test concepts 83–4, 85, 89, 91–5 contingency tables 92–5 examples 83–4, 85, 89, 91–2 goodness of fit test 91–5 multi-way tables 94–5 tables 84, 91 Chu Shi-Chieh’s Ssu Yuan Y Chien 56 circles, tree diagrams 30–5 class intervals concepts 13–20, 44–5, 63–4, 241–7 histograms 13–20, 44–5 mean calculations 44–5 mid-points 44–5, 241–7 notation 13–14, 20 Sturges’s formula 20 variance calculations 44–5 classical approach, probability theory 22, 27 cluster sampling 50 coin-tossing examples, probability theory 21–3, 53–4 collection techniques, data 17, 47–52, 129–47 colours, graphical presentational approaches 9 combination, probability distribution (density) functions 54–8 common logarithm (base 10) 20 communications, decisions 189–90 comparative data, bar charts 10–12 comparative histograms see also histograms examples 14–19 completed goods 195 see also stock . . . conditional probability, concepts 25–7, 35 confidence intervals, concepts 71, 75–81, 105, 109, 116–20, 190, 262–5 constraining equations, linear programming 159–70 contingency tables, concepts 92–5 continuous approximation, stock control 200–1 continuous case, failures 251 continuous data concepts 7, 13–14, 44–5, 65–6, 251 histograms 7, 13–14 continuous uniform distribution, concepts 64–6 correlation coefficient concepts 104–20, 261–5, 268–9 critical value 105–6, 113–20 equations 104–5 examples 105–8, 115–20 costs capital 219–25, 229–30 dynamic programming 180–82 ghost costs 172–7 holding costs 182–5, 197–201, 204–8 linear programming 167–70, 171–7 sampling 47 stock control 182–5, 195–201 transport problems 171–7 trend analysis 236–47 types 167–8, 182 counting techniques, probability distribution (density) functions 54 covariance see also correlation coefficient concepts 104–20, 263–5 credit cards 159–66, 267–9 credit derivatives 97 see also derivatives Index credit risk, modelling 75, 149, 261–5 critical value, correlation coefficient 105–6, 113–20 cumulative frequency polygons concepts 13–20, 39–40, 203 examples 14–20 uses 13–14 current costs, linear programming 167–70 cyclical variations, trends 238–47 data analysis methods 47–52, 129–47, 271–4 collection techniques 17, 47–52, 129–47 continuous/discrete types 7–12, 13–14, 44–5, 53–5, 65–6, 72, 251 design/approach to analysis 129–47 errors 129–47 graphical presentational approaches 1–20, 149–57 identification 2–5, 261–5 Latin squares 131–2, 143–7 loss data 267–9, 271–4 neural networks 275–7 qualities 17, 47 randomised block design 129–35 reliability and accuracy 17, 47 sampling 17, 47–52 time series 235–47 trends 5, 10, 235–47 two-way classification analysis 135–47 data points, scatter plots 2–5 databases, loss databases 272–4 debentures 149–57 decisions alternatives 191–4 Bayes’theorem 27–30, 31 communications 189–90 concepts 21–35, 189–94, 215–25, 228–34, 249–60 courses of action 191–2 definition 21 delegation 189–90 empowerment 189–90 guesswork 191 lethargy pitfalls 189 minimax regret rule 192–4 modelling problems 189–91 Monty Hall problem 34–5, 212–13 pitfalls 189–94 probability theory 21–35, 53–66, 189–94, 215–18 problem definition 129, 190–2 project analysis guidelines 190–2, 219–25, 228–34 replacement of assets 215–18, 249–60 staff 189–90 287 steps 21 stock control 195–201, 203–8 theory 189–94 degrees of freedom 70–1, 75–89, 91–5, 110–20, 136–7 ANOVA (analysis of variance) 110–20, 121–7, 136–7 concepts 70–1, 75–89, 91–5, 110–20, 136–7 delegation, decisions 189–90 density functions see also probability distribution (density) functions concepts 65–6, 67, 83–4 dependent variables, concepts 2–5, 103–20, 235 derivatives 58, 97–8, 272 see also credit . . . ; options design/approach to analysis, data 129–47 dice-rolling examples, probability theory 21–3, 53–5 differentiation 251 discount factors adjusted discount rates 228–9 net present value (NPV) 220–1, 228–9, 231–2 discrete data bar charts 7–12, 13 concepts 7–12, 13, 44–5, 53–5, 72 discrete uniform distribution, concepts 53–5 displays see also presentational approaches data 1–5 Disraeli, Benjamin 1 division notation 280, 282 dynamic programming complex examples 184–7 concepts 179–87 costs 180–82 examples 180–87 principle of optimality 179–87 returns 179–80 schematic 179–80 ‘travelling salesman’ problem 185–7 e-mail surveys 50–1 economic order quantity see also stock control concepts 195–201 examples 196–9 empowerment, staff 189–90 error sum of the squares (SSE), concepts 122–5, 133–47 errors, data analysis 129–47 estimates mean 76–81 probability theory 22, 25–6, 31–5, 75–81 Euler, L. 131 288 Index events independent events 22–4, 35, 58, 60, 92–5 mutually exclusive events 22–4, 58 probability theory 21–35, 58–66, 92–5 scenario analysis 40, 193–4, 271–4 tree diagrams 30–5 Excel 68, 206–7 exclusive events see mutually exclusive events expected errors, sensitivity analysis 268–9 expected value, net present value (NPV) 231–2 expert systems 275 exponent notation 282–4 exponential distribution, concepts 65–6, 209–10, 252–5 external fraud 272–4 extrapolation 119 extreme value distributions, VaR 262–4 F distribution ANOVA (analysis of variance) 110–20, 127, 134–7 concepts 85–9, 110–20, 127, 134–7 examples 85–9, 110–20, 127, 137 tables 85–8 f notation 8–9, 13–20, 26, 38–9, 44–5, 65–6, 85 factorial notation 53–5, 283–4 failure probabilities see also reliability replacement of assets 215–18, 249–60 feasibility polygons 152–7, 163–4 finance selection, linear programming 164–6 fire extinguishers, ANOVA (analysis of variance) 123–7 focus groups 51 forward recursion 179–87 four by four tables 94–5 fraud 272–4, 276 Fréchet distribution 262 frequency concepts 8–9, 13–20, 37–45 cumulative frequency polygons 13–20, 39–40, 203 graphical presentational approaches 8–9, 13–20 frequentist approach, probability theory 22, 25–6 future cash flows 219–25, 227–34, 240–1 fuzzy logic 276 Garbage In, Garbage Out (GIGO) 261–2 general rules, linear programming 167–70 genetic algorithms 276 ghost costs, transport problems 172–7 goodness of fit test, chi-squared test 91–5 gradient (a notation), linear regression 103–4, 107–20 graphical method, linear programming 149–57, 163–4 graphical presentational approaches concepts 1–20, 149–57, 235–47 rules 8–9 greater-than notation 280–4 Greek alphabet 283 guesswork, modelling 191 histograms 2, 7, 13–20, 41, 73 class intervals 13–20, 44–5 comparative histograms 14–19 concepts 7, 13–20, 41, 73 continuous data 7, 13–14 examples 13–20, 73 skewness 41 uses 7, 13–20 holding costs 182–5, 197–201, 204–8 home insurance 10–12 Hopfield 275 horizontal axis bar charts 8–9 histograms 14–20 linear regression 103–4, 107–20 scatter plots 2–5, 103 hypothesis testing concepts 77–81, 85–95, 110–27 examples 78–80, 85 type I and type II errors 80–1 i notation 8–9, 13–20, 28–30, 37–8, 103–20 identification data 2–5, 261–5 trends 241–7 identity rule 282 impact assessments 21, 271–4 independent events, probability theory 22–4, 35, 58, 60, 92–5 independent variables, concepts 2–5, 70, 103–20, 235 infinity, normal distribution 67–72 information, quality needs 190–4 initial solution, linear programming 167–70 insurance industry 10–12, 29–30 integers 280–4 integration 65–6, 251 intercept (b notation), linear regression 103–4, 107–20 interest rates base rates 240 daily movements 40, 261 project evaluation 219–25, 228–9 internal rate of return (IRR) concepts 220–2, 223–5 examples 220–2 interpolation, IRR 221–2 interviews, uses 48, 51–2 inventory control see stock control Index investment strategies 149–57, 164–6, 262–5 IRR see internal rate of return iterative processes, linear programming 170 j notation 28–30, 37, 104–20, 121–2 JP Morgan 263 k notation 20, 121–7 ‘know your customer’ 272 Kohonen self-organising maps 275 Latin squares concepts 131–2, 143–7 examples 143–7 lead times, stock control 195–201 learning strategies, neural networks 275–6 less-than notation 281–4 lethargy pitfalls, decisions 189 likelihood considerations, scenario analysis 272–3 linear programming additional variables 167–70 concepts 149–70 concerns 170 constraining equations 159–70 costs 167–70, 171–7 critique 170 examples 149–57, 159–70 finance selection 164–6 general rules 167–70 graphical method 149–57, 163–4 initial solution 167–70 iterative processes 170 manual preparation 170 most profitable loans 159–66 optimal advertising allocation 154–7 optimal investment strategies 149–57, 164–6 returns 149–57, 164–6 simplex method 159–70, 171–2 standardisation 167–70 time constraints 167–70 transport problems 171–7 linear regression analysis 110–20 ANOVA (analysis of variance) 110–20 concepts 3, 103–20 equation 103–4 examples 107–20 gradient (a notation) 103–4, 107–20 intercept (b notation) 103–4, 107–20 interpretation 110–20 notation 103–4 residual sum of the squares 109–20 slope significance test 112–20 uncertainties 108–20 literature searches, surveys 48 289 loans finance selection 164–6 linear programming 159–66 risk assessments 159–60 log-normal distribution, concepts 257–8 logarithms (logs), types 20, 61 losses, banks 267–9, 271–4 lotteries 22 lower/upper quartiles, concepts 39–41 m notation 55–8 mail surveys 48, 50–1 management information, graphical presentational approaches 1–20 Mann–Whitney test see U test manual preparation, linear programming 170 margin of error, project evaluation 229–30 market prices, VaR 264–5 marketing brochures 184–7 mathematics 1, 7–8, 196–9, 219–20, 222–5, 234, 240–1, 251, 279–84 matrix plots, concepts 2, 4–5 matrix-based approach, transport problems 171–7 maximum and minimum, concepts 37–9, 40, 254–5 mean comparison of two sample means 79–81 comparisons 75–81 concepts 37–45, 59–60, 65–6, 67–74, 75–81, 97–8, 100–2, 104–27, 134–5 confidence intervals 71, 75–81, 105, 109, 116–20, 190, 262–5 continuous data 44–5, 65–6 estimates 76–81 hypothesis testing 77–81 linear regression 104–20 normal distribution 67–74, 75–81, 97–8 sampling 75–81 mean square causes (MSC), concepts 122–7, 134–47 mean square errors (MSE), ANOVA (analysis of variance) 110–20, 121–7, 134–7 median, concepts 37, 38–42, 83, 98–9 mid-points class intervals 44–5, 241–7 moving averages 241–7 minimax regret rule, concepts 192–4 minimum and maximum, concepts 37–9, 40 mode, concepts 37, 39, 41 modelling banks 75–81, 85, 97, 267–9, 271–4 concepts 75–81, 83, 91–2, 189–90, 195–201, 215–18, 261–5 decision-making pitfalls 189–91 economic order quantity 195–201 290 Index modelling (cont.) guesswork 191 neural networks 275–7 operational risk 75, 262–5, 267–9, 271–4 output reviews 191–2 replacement of assets 215–18, 249–60 VaR 261–5 moments, density functions 65–6, 83–4 money laundering 272–4 Monte Carlo simulation bank cashier problem 209–12 concepts 203–14, 234 examples 203–8 Monty Hall problem 212–13 queuing problems 208–10 random numbers 207–8 stock control 203–8 uses 203, 234 Monty Hall problem 34–5, 212–13 moving averages concepts 241–7 even numbers/observations 244–5 moving totals 245–7 MQMQM plot, concepts 40 MSC see mean square causes MSE see mean square errors multi-way tables, concepts 94–5 multiplication notation 279–80, 282 multiplication rule, probability theory 26–7 multistage sampling 50 mutually exclusive events, probability theory 22–4, 58 n notation 7, 20, 28–30, 37–45, 54–8, 103–20, 121–7, 132–47, 232–4 n!

Pascal’s triangle, concepts 56–7 payback period, concepts 219, 222–5 PCs see personal computers people costs 167–70 perception 275 permutation, probability distribution (density) functions 55 personal computers (PCs) 7–9, 58–60, 130–1, 198–9, 208–10, 215–18, 253–5 pictures, words 1 pie charts concepts 7, 12 critique 12 examples 12 planning, data collection techniques 47, 51–2 plot, concepts 1, 10 plus or minus sign notation 279 Poisson distribution concepts 58–66, 72–3, 91–2, 200–1, 231–2 examples 58–65, 72–3, 91–2, 200–1 net present value (NPV) 231–2 normal distribution 72–3 stock control 200–1 suicide attempts 62–5 uses 57, 60–5, 72–3, 91–2, 200–1, 231–2 291 population considerations, sampling 47, 49–50, 75–95, 109, 121–7 portfolio investments, VaR 262–5 power notation 282–4 predictions, neural networks 276–7 presentational approaches concepts 1–20 good presentation 1–2 management information 1–20 rules 8–9 trends 5, 10, 235–47 price/earnings ratio (P/E ratio), concepts 222 principle of optimality, concepts 179–87 priors, concepts 28–30 Prob notation 21–35, 68–70, 254–5 probability distribution (density) functions see also normal distribution binomial distribution 55–8, 61–5, 71–2, 98–9, 231–2 combination 54–8 concepts 53–95, 203, 205, 231–2, 257–60 continuous uniform distribution 64–6 counting techniques 54 discrete uniform distribution 53–5, 72 examples 53–5 exponential distribution 65–6, 209–10, 252–5 log-normal distribution 257–8 net present value (NPV) 231–2 permutation 55 Poisson distribution 58–66, 72–3, 91–2, 200–1, 231–2 probability theory addition rule 24–5 Bayes’theorem 27–30, 31 classical approach 22, 27 coin-tossing examples 21–3, 53–4 concepts 21–35, 53–66, 200–1, 203, 215–18, 231–2 conditional probability 25–7, 35 decisions 21–35, 53–66, 189–94, 215–18 definitions 22 dice-rolling examples 21–3, 53–5 estimates 22, 25–6, 32–5, 75–81 event types 22–4 examples 25–35, 53–5 frequentist approach 22, 25–6 independent events 22–4, 35, 58, 60, 92–5 Monty Hall problem 34–5, 212–13 multiplication rule 26–7 mutually exclusive events 22–4, 58 notation 21–2, 24–30, 54–5, 68–9, 75–6, 79–81, 83–5, 99–104, 121–2, 131–5, 185–7, 254–5 overlapping probabilities 25 simple examples 21–2 subjective approach 22 292 Index probability theory (cont.) tree diagrams 30–5 Venn diagrams 23–4, 28 problems, definition importance 129, 190–2 process costs 167–70 production runs 184–7 products awaiting shipment 195 see also stock . . . profit and loss accounts, stock 195 profitable loans, linear programming 159–66 projects see also decisions alternatives 191–4, 219–25 analysis guidelines 190–2, 219–25, 228–34 break-even analysis 229–30 courses of action 191–2 evaluation methods 219–25, 227, 228–34 finance issues 164–6 guesswork 191 IRR 220–2, 223–5 margin of error 229–30 net present value (NPV) 219–22, 228–9, 231–2 P/E ratio 222 payback period 219, 222–5 returns 164–6, 219–25, 227–34 sponsors 190–2 quality control 61–4 quality needs, information 190–4 quartiles, concepts 39–41 questionnaires, surveys 48, 50–1 questions, surveys 48, 51–2, 97 queuing problems, Monte Carlo simulation 208–10 quota sampling 50 r! notation 54–5 r notation 104–20, 135–47 random numbers, Monte Carlo simulation 207–8 random samples 49–50 random walks see also Brownian motion concepts 22 randomised block design ANOVA (analysis of variance) 134–5, 141–3 concepts 129–35 examples 130–1, 140–3 parameters 132–5 range, histograms 13–20 ranks, U test 99–102 raw materials 195 see also stock . . . reciprocals, numbers 280–4 recursive calculations 56–8, 61–2, 179–87 regrets, minimax regret rule 192–4 relative frequencies, concepts 8–12, 14–20 relevance issues, scenario analysis 272, 273–4 reliability bathtub curves 249–51 concepts 17, 47, 215–18, 249–60 continuous case 251 data 17, 47 definition 251 examples 249 exponential distribution 252–5 obsolescence 215–18 systems/components 215–18, 249–60 Weibull distribution 255–7, 262 reorder levels, stock control 195–201 replacement of assets 215–18, 249–60 reports, formats 1 residual sum of the squares, concepts 109–20, 121–7, 132–47 returns dynamic programming 179–80 IRR 220–2, 223–5 linear programming 149–57, 164–6 net present value (NPV) 219–22, 228–9, 231–2 optimal investment strategies 149–57, 164–6 P/E ratio 222 payback period 219, 222–5 projects 164–6, 219–25, 227–34 risk/uncertainty 227–34 risk adjusted cash flows 228–9 adjusted discount rates 228–9 Basel Accord 262, 267–9, 271 concepts 28–30, 159–66, 227–34, 261–5, 267–9, 271–4 definition 227 loan assessments 159–60 management 28–30, 159–66, 227–34, 261–5, 267–9, 271–4 measures 232–4, 271–4 net present value (NPV) 228–9, 231–2 operational risk 27–8, 75, 262–5, 267–9, 271–4 profiles 268–9 scenario analysis 40, 193–4, 271–4 sensitivity analysis 40, 264–5, 267–9 uncertainty 227–34 VaR 261–5 RiskMetrics 263 rounding 281–4 sample space, Venn diagrams 23–4, 28 sampling see also surveys analysis methods 47–52, 129–47 bad examples 50–1 bias 17, 47–50, 51–2, 97, 129–35 cautionary notes 50–2 Index central limit theorem 70, 75 cluster sampling 50 comparison of two sample means 79–81 concepts 17, 47–52, 70, 75–95, 109, 121–7, 129–47 costs 47 hypothesis testing 77–81, 85–95 mean 75–81 multistage sampling 50 normal distribution 70–1, 75–89 planning 47, 51–2 population considerations 47, 49–50, 75–95, 109, 121–7 problems 50–2 questionnaires 48, 50–1 quota sampling 50 random samples 49–50 selection methods 49–50, 77 size considerations 49, 77–8, 129 stratified sampling 49–50 systematic samples 49–50 units of measurement 47 variables 47 variance 75–81, 83–9, 91–5 scaling, scenario analysis 272 scatter plots concepts 1–5, 103–4 examples 2–3 uses 3–5, 103–4 scenario analysis anonimised databases 273–4 concepts 40, 193–4, 271–4 likelihood considerations 272–3 relevance issues 272, 273–4 scaling 272 seasonal variations, trends 236–40, 242–7 security costs 167–70 selection methods, sampling 49–50, 77 semantics 33–4 sensitivity analysis, concepts 40, 264–5, 267–9 sets, Venn diagrams 23–4, 28 sign test, concepts 98–9 significant digits 281–4 simplex method, linear programming 159–70, 171–2 simulation, Monte Carlo simulation 203–14, 234 size considerations, sampling 49, 77–8, 129 skewness, concepts 41–5 slope significance test see also a notation (gradient) linear regression 112–20 software packages reports 1 stock control 198–9 293 sponsors, projects 190–2 spread, standard deviation 41–5 square root 282–4 SS see sum of the squares SSC see sum of the squares for the causes SST see sum of the squares of the deviations Ssu Yuan Y Chien (Chu Shi-Chieh) 56 staff decision-making processes 189–90 training needs 189 standard deviation see also variance cash flows 232–4 concepts 41–5, 67–81, 83, 97–8, 102, 104–20, 232–4 correlation coefficient 104–20 examples 42–5, 232–4 normal distribution 67–81, 83, 97–8, 102, 232–4 uses 41–5, 104–20, 232–4 standard terms, statistics 37–45 standardisation, linear programming 167–70 statistical terms 1, 37–45 concepts 1, 37–45 maximum and minimum 37–9, 40, 254–5 mean 37–45 median 37, 38–42 mode 37, 39, 41 MQMQM plot 40 skewness 41–5 standard deviation 41–5 standard terms 37–45 upper/lower quartiles 39–41 variance 41–5 statistics, concepts 1, 37–45 std(x) notation (standard deviation) 42–5 stock control concepts 195–201, 203–8 continuous approximation 200–1 costs 182–5, 195–201 economic order quantity 195–201 holding costs 182–5, 197–201, 204–8 lead times 195–201 Monte Carlo simulation 203–8 non-zero lead times 199–201 order costs 197–201 Poisson distribution 200–1 variable costs 197–201 volume discounts 199–201 stock types 195 stratified sampling 49–50 Sturges’s formula 20 subjective approach, probability theory 22 subtraction notation 279 successful products, tree diagrams 30–3 suicide attempts, Poisson distribution 62–5 294 Index sum of the squares for the causes (SSC), concepts 122–5, 133–47 sum of the squares of the deviations (SST), concepts 122–5 sum of the squares (SS) ANOVA (analysis of variance) 110–20, 121–7, 134–5 concepts 109–20, 121–7, 132, 133–47 supply/demand matrix 171–7 surveys see also sampling bad examples 50–1 cautionary notes 50–2 concepts 48–52, 97 interviews 48, 51–2 literature searches 48 previous surveys 48 problems 50–2 questionnaires 48, 50–1 questions 48, 51–2, 97 symmetry, skewness 41–5, 67–9, 75–6, 98–9 systematic errors 130 systematic samples 49–50 systems costs 167–70 t statistic concepts 75–81, 97–8, 114–20, 121, 123, 125, 127 tables 75, 81 tables ANOVA (analysis of variance) 110–11, 121–3, 134–47 chi-squared test 84, 91 contingency tables 92–5 F distribution 85–8 normal distribution 67, 74 t statistic 75, 81 tabular formats, reports 1 telephone surveys 50–2 text surveys 50–1 three-dimensional graphical representations 9 time constraints, linear programming 167–70 time series concepts 235–47 cyclical variations 238–47 mathematics 240–1 moving averages 241–7 seasonal variations 236–40, 242–7 Z charts 245–7 trade finance 164–6 training needs, communications 189 transport problems concepts 171–7 ghost costs 172–7 ‘travelling salesman’ problem, dynamic programming 185–7 tree diagrams examples 30–4 Monty Hall problem 34–5 probability theory 30–5 trends analysis 235–47 concepts 235–47 cyclical variations 238–47 graphical presentational approaches 5, 10, 235–47 identification 241–7 mathematics 240–1 moving averages 241–7 seasonal variations 236–40, 242–7 Z charts 245–7 true rank, U test 99–102 truncated normal distribution, concepts 259, 260 truncation concepts, scatter plots 2–3 Twain, Mark 1 two-tail test, hypothesis testing 77–81, 109 two-way classification analysis 135–47 examples 137–40 type I and type II errors examples 80–1 hypothesis testing 80–1 U test, concepts 99–102 uncertainty concepts 108–20, 227–34 definition 227 linear regression 108–20 net present value (NPV) 228–9, 231–2 risk 227–34 upper/lower quartiles, concepts 39–41 valuations, options 58, 97–8 value at risk (VaR) calculation 264–5 concepts 261–5 examples 262–3 extreme value distributions 262–4 importance 261 variable costs, stock control 197–201 variables bar charts 7–8 concepts 2–3, 7–12, 13–14, 27–35, 70, 103–20, 121–7 continuous/discrete types 7–12, 13–14, 44–5, 53–5, 65–6, 72, 251 correlation coefficient 104–20 data collection techniques 47 dependent/independent variables 2–5, 70, 103–20, 235 histograms 13–20 Index linear programming 149–70 linear regression 3, 103–20 scatter plots 2–5 sensitivity analysis 40, 264–5, 267–9 variance see also standard deviation ANOVA (analysis of variance) 110–20, 121–7, 134–47 chi-squared test 83–4, 85, 89, 91–5 comparisons 83–9 concepts 41–5, 65–6, 67, 75–81, 83–9, 91–5, 102, 104, 107, 110–20, 233–4, 263–5 continuous data 44–5 covariance 104–20, 263–5 examples 42–5 F distribution 85–9, 110–20, 127, 134–7 linear regression 104, 107, 110–20 var(x) notation (variance) 42–5, 233–4 VC see venture capital 295 Venn diagrams, concepts 23–4, 28 venture capital (VC) 149–57 vertical axis bar charts 8–9 histograms 14–20 linear regression 103–4, 107–20 scatter plots 2–5, 103 volume discounts, stock control 199–201 Weibull distribution concepts 255–7, 262 examples 256–7 ‘what/if’ analysis 33 Wilcoxon test see U test words, pictures 1 work in progress 195 Z charts, concepts 245–7 z notation 67–74, 102, 105, 234 zero factorial 54–5 Index compiled by Terry Halliday


pages: 261 words: 86,261

The Pleasure of Finding Things Out: The Best Short Works of Richard P. Feynman by Richard P. Feynman, Jeffrey Robbins

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Albert Einstein, Brownian motion, impulse control, index card, John von Neumann, Murray Gell-Mann, pattern recognition, Richard Feynman, Richard Feynman, Richard Feynman: Challenger O-ring, the scientific method

I speak, of course, “in principle,” and I am not speaking about the actual manufacture of such devices. Let us therefore discuss what happens if we try to make the devices as small as possible. Reducing the Size FIGURE 5 So my third topic is the size of computing elements and now I speak entirely theoretically. The first thing that you would worry about when things get very small is Brownian motion*—everything is shaking about and nothing stays in place. How can you control the circuits then? Furthermore, if a circuit does work, doesn’t it now have a chance of accidentally jumping back? If we use two volts for the energy of this electric system, which is what we ordinarily use (Fig. 5), that is eighty times the thermal energy at room temperature (kT = 1/40 volt) and the chance that something jumps backward against 80 times thermal energy is e, the base of the natural logarithm, to the power minus eighty, or 10-43.

If the things flip back and then go forward later it is still all right. It’s very much the same as a particle in a gas which is bombarded by the atoms around it. Such a particle usually goes nowhere, but with just a little pull, a little prejudice that makes a chance to move one way a little higher than the other way, the thing will slowly drift forward and travel from one end to the other, in spite of the Brownian motion that it has made. So our computer will compute provided we apply a drift force to pull the thing across the calculation. Although it is not doing the calculation in a smooth way, nevertheless, calculating like this, forward and backward, it eventually finishes the job. As with the particle in the gas, if we pull it very slightly, we lose very little energy, but it takes a long time to get to one side from the other.

., 39, 40, 43 Bessel functions, 223 Beta decay, 192 Bethe, Hans, 11, 60–61, 64, 86, 190, 197–198, 235 Bets, 69 Big Bang, 199, 200 Biology, 99, 100, 101, 105, 123–124, 124–125, 126, 241. See also under Chemistry Black holes, 229(n) Bohr, Aage, 86, 87 Bohr, Niels, 86–88, 190, 203 Bongos, 191 Books of the world, 121–122 Bose-Einstein condensate, xvii Brains, 145, 194, 218, 222. See also Computers, analogy with brains Brass, 90 Brave New World (Huxley), 99 Bridgman, Percy, 118 British Museum Library, 121 Brownian motion, 38–39, 38(fig.), 42 Buddhism, 142 Cadmium, 74, 76 Calculus, 6–7, 195 California Institute of Technology (Caltech), 13, 191–192, 205–216, 226, 232–233 Caltech Cosmic Cube, 30 Cargo cults, 187, 242–243. See also Science, Cargo Cult Science Cathode ray oscilloscope, 120 Catholic Church, 7, 98, 111, 112–113 Censorship. See under Los Alamos Certainty. See Uncertainty Challenger. See Space Shuttle Challenger Chemistry and biology, 137, 138 chemical analysis/synthesis, 125, 137–138 chemical reactions, 131, 218 Chess, 48 chess game analogy, 13–14, 14–15 Chicago, 56–57 Children, 21–22, 145–146, 172 Christ, divinity of, 251, 254 Christie, Bob, 62, 73, 83 Communication, 113, 147 Communism, 251–252 Compton, 55, 56 Computers, 27–52, 126–129, 194 analogy with brains, 46–48 central processors, 29, 30–31 on Challenger Orbiter, 164–168 chips in, 28–29, 44 clock time vs. circuit time in, 35 debugging, 28 energy consumption of, 29, 32–37, 38, 42, 43, 44, 50–51 gates, reversible/irreversible, 39–40, 41(fig.), 43, 50.


pages: 445 words: 105,255

Radical Abundance: How a Revolution in Nanotechnology Will Change Civilization by K. Eric Drexler

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3D printing, additive manufacturing, agricultural Revolution, Bill Joy: nanobots, Brownian motion, carbon footprint, Cass Sunstein, conceptual framework, crowdsourcing, dark matter, double helix, failed state, global supply chain, industrial robot, iterative process, Mars Rover, means of production, Menlo Park, mutually assured destruction, New Journalism, performance metric, reversible computing, Richard Feynman, Richard Feynman, Silicon Valley, South China Sea, Thomas Malthus, V2 rocket, Vannevar Bush

The idea of atoms, of course, had been around since antiquity. In Greece circa 400 BCE Democritus argued that matter must ultimately consist of indivisible particles—as indeed atoms are, barring nuclear reactions. In Rome circa 50 BCE Lucretius argued the same case in considerable depth and suggested that dust motes that could be seen dancing in sunbeams were, in fact, driven by what is now called “Brownian motion,” the effect of collisions with atoms (and for some of the motions he saw, he was right). Today, the most advanced forms of atomically precise fabrication rely on this Brownian dance to move molecules. After classical times, centuries passed before any further progress was achieved in understanding the atomic basis of the material world. Inquiry reached a landmark in England in the early 1800s when John Dalton observed that chemical reactions combined substances in fixed proportions and explained these proportions in terms of atoms.

PART 5 THE TRAJECTORY OF TECHNOLOGY CHAPTER 12 Today’s Technologies of Atomic Precision HUMAN TECHNOLOGY EVENTUALLY LED to machines, yet it began with wood, hide, stones, and hands—which is to say, with biopolymers (cellulose, collagen) and harder, inorganic materials used to make hand-held tools. AP nanotechnologies are following a similar path, but with AP control of biopolymers and inorganic materials using assembly driven by Brownian motion rather than hands. Once again, advances will lead to machines for making things. Just as an early blacksmith’s hammer and tongs differ from an automated machine in a watch-making factory, today’s early tools differ greatly from advanced APM systems. And just as blacksmith-level technology led to today’s machines, so today’s AP molecular technologies will lead to tomorrow’s nanomachines. Where do we stand today on the road to advanced atomically precise fabrication, the road that leads to APM?

To understand the next steps and the road ahead, it’s important to understand how self-assembly and stereotactic methods can be combined in complementary ways. Today’s Self-Assembly Methods Self-assembly has one great advantage: Because it employs thermal motion to move parts into place, assembling parts requires no nanoscale machinery. Researchers can use conventional biological or chemical means to make the parts, and if they’re properly designed, thermally driven Brownian motion can do the rest. Self-assembly, however, also brings with it a set of challenges and limitations. To produce complex, non-repetitive structures by self-assembly, each part must bind in just one specific place and position as the structure comes together, and this means that each part must have a unique shape, like a piece of a jigsaw puzzle. These molecular puzzle pieces can’t be too small, or they’d be too simple and too much alike; they can’t bind too strongly, or near-matches would end up in the wrong places and never let go; and like a finished jigsaw puzzle, the end product would be divided by many irregular seams.


pages: 287 words: 87,204

Erwin Schrodinger and the Quantum Revolution by John Gribbin

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Albert Einstein, Albert Michelson, All science is either physics or stamp collecting, Arthur Eddington, British Empire, Brownian motion, double helix, Drosophila, Edmond Halley, Ernest Rutherford, Fellow of the Royal Society, Henri Poincaré, Isaac Newton, John von Neumann, Richard Feynman, Richard Feynman, Schrödinger's Cat, Solar eclipse in 1919, The Present Situation in Quantum Mechanics, the scientific method, trade route, upwardly mobile

He spent the winter of 1914–15 there, enjoying the beautiful mountain scenery while the conflict on the Western Front settled into the grim trench warfare for which the First World War is best remembered by Britain and the other Western participants. His next posting was to the equally peaceful, but less scenic, garrison town of Komárom, between Vienna and Budapest. There, Schrödinger wrote a paper about the behaviour of small particles being jostled in a fluid (gas or liquid) by the impact of molecules of the fluid. This is known as Brownian motion, after the Scottish physicist Robert Brown (1773–1858), who studied it in the 1820s. In 1905, Albert Einstein had proved that this erratic jittering can be explained statistically as caused by the constant but uneven bombardment that particles such as pollen grains receive from atoms and molecules, and thereby provided compelling evidence for the reality of atoms—just too late for this to be much comfort to Boltzmann.1 In a quite separate investigation, culminating in 1912, the American Robert Andrews Millikan (1868–1953)—who also, incidentally, coined the term “cosmic rays”—had managed to measure the charge on the electron by monitoring the way tiny electrically charged droplets of water or oil drift in an electric field.

In 1905, Albert Einstein had proved that this erratic jittering can be explained statistically as caused by the constant but uneven bombardment that particles such as pollen grains receive from atoms and molecules, and thereby provided compelling evidence for the reality of atoms—just too late for this to be much comfort to Boltzmann.1 In a quite separate investigation, culminating in 1912, the American Robert Andrews Millikan (1868–1953)—who also, incidentally, coined the term “cosmic rays”—had managed to measure the charge on the electron by monitoring the way tiny electrically charged droplets of water or oil drift in an electric field. These droplets are small enough to be affected by Brownian motion, and Schrödinger analysed statistically the importance of these effects in Millikan-type experiments. Nothing dramatic came out of the study, but it is important in the context of Schrödinger’s career because it was his first published foray into statistics, which would later loom large in his work. By the time this paper was published, the war, and Schrödinger, had both moved on. Italy was persuaded to join the Triple Entente with promises of large chunks of Austria, and declared war on 23 May 1915.

.: Addison-Wesley, 1980) Zeilinger, Anton, Dance of the Photons (New York: Farrar, Strauss & Giroux, 2010) Index action at a distance Aharonov, Yakir Aigentler, Henriette von Alpbach American Philosophical Society Anderson, Carl Annalen der Physik Annales de physique anti-particles Arosa Arzberger, Hans Arzberger, Rhoda (née Bauer, aunt) Aspect, Alain atoms: Bohr model; Boltzmann’s work; concept; Copenhagen Interpretation; decoherence; Einstein’s work; entanglement experiments; “green pamphlet”; Mach’s view; Maxwell’s work; nuclear model; Planck’s work; Poincaré’s work; quantum chemistry; quantum computing; quantum physics; quantum spin of electron; quantum teleportation experiments; Rutherford’s work; Schrödinger’s work; structure Austria: Anschluss (1938); army; First World War and aftermath; International Atomic Energy Agency representation; Nazism; religion; Schrödinger’s flight from; Schrödinger’s return to; Second World War aftermath Austria-Hungary Austrian Empire Austrian Physical Society Baird, John Logie Ballot, Christoph Buys Bamberger, Emily (Minnie, née Bauer, aunt) Bamberger, Helga (cousin) Bamberger, Max Bär, Richard Bauer, Alexander (grandfather) Bauer, Alexander (great-grandfather) Bauer, Emily (Minnie, aunt), see Bamberger Bauer, Emily (Minnie, née Russell, grandmother) Bauer, Friedrich (Fritz) Bauer, Georgie, see Schrödinger Bauer, Johanna (Hansi), see Bohm Bauer, Josepha (née Wittmann-Denglass, great-grandmother) Bauer, Rhoda (aunt), see Arzberger BBC Becquerel, Henri Bell, John Bell’s inequality Bennett, Charles Berlin: Academy of Sciences; Kaiser Wilhelm Institute for Chemistry; Schrödinger’s departure; Schrödinger’s professorship; Schrödinger’s work; University of Bernstein, Jeremy Bertel, Annemarie (Anny), see Schrödinger Besso, Michele birds, vision Bitbol, Michel Blackett, Patrick Blair, Linda Bloch, Felix Bohm, David Bohm, Franz Bohm, Johanna (Hansi, née Bauer): escape from Austria to London; escape from Germany to London; marriage; memories of Schrödinger; pregnancy; relationship with Schrödinger; in Vienna Bohr, Niels: on collapse of wave function; on complementarity; Copenhagen Institute; Copenhagen Interpretation; Einstein’s views of his work; Festival; honours; influence; “Light and Life” lecture; model of the atom; Nobel Prize; quantization rules; relationship with Schrödinger; Schrödinger’s views of his work; work with Heisenberg Boltzmann, Ludwig: background; career; depression; education; on entropy; influence on Schrödinger; on international nature of physics; marriage; relationship with Mach; research; statistical approach; Stefan–Boltzmann Law of black body radiation; suicide; work on atoms; work on thermodynamics Born, Max: background and education; in Cambridge; career; on chance and probability; on Copenhagen school; on Dirac’s work; Edinburgh professorship; in Göttingen; Heisenberg’s studies; in Italy; matrix mechanics; Natural Philosophy of Cause and Chance; Nobel controversy; Nobel Prize; on quantum mechanics; quantum revolution; relationship with Schrödinger; retirement; sacked under Nazis; Schrödinger’s response to his work; statistics; on von Neumann’s work; work on wave function Bose, Satyendra Nath Bose–Einstein statistics bosons Bragg, Lawrence Bragg, William Braunizer, Andreas (grandson) Braunizer, Arnulf Braunizer, Ruth (née March, daughter): in Belgium; birth; birth of son; care of Arthur; in Dublin; in Graz; half-sisters; in Innsbruck; marriage; in Oxford; pregnancy; relationship with Anny; relationship with father; relationship with mother Brecht, Bertolt Breslau Bristol University Brown, Robert Browne, Monsignor Paddy Brownian motion Bunsen, Robert Cahill & Company California: Institute of Technology; University of Cambridge: Born in; Cavendish Laboratory; Heisenberg’s lectures; Maxwell at; Newton at; Philosophical Society; Schrödinger’s visits; Tarner Lectures Cambridge University Press (CUP) “Can Quantum Mechanical Description of Physical Reality Be Considered Complete?”(EPR paper) CERN Charles, Emperor Chemical and Engineering News Chemical–Physical Society Chicago chromosomes Clauser, John Clausius, Rudolf cloud chamber Cockcroft, John Cold War colour vision Columbia University Como conference (1927) complementarity Compton, Arthur Compton effect Condon, Edward Congress of Vienna (1913) Copenhagen, Niels Bohr Institute Copenhagen Interpretation; author’s view; Bell’s view; Bohm’s view; Born on; consensus view; Einstein’s view; origins; package; predictions; presentation; probability in; Schrödinger’s view Cosmic Code, The (Pagels) cosmic rays cosmology Cramer, John Crick, Francis cryptography Curie, Marie and Pierre Czernowitz D-Wave Systems Darwin, Charles Darwin, Charles (grandson of above) Davies, Paul Davy, Humphry de Broglie, Louis: background and education; Einstein’s view of his work; influence; pilot wave model; Solvay Congress; thesis de Broglie, Maurice De magnete (Gilbert) De motu corporum in gyrum (Newton) de Valera, Éamon (“Dev”): background and career; Dublin Institute for Advanced Studies; invitation to Schrödinger; Schrödinger’s departure; Schrödinger’s lectures de Valera, Sinéad (née Flanagan) Debye, Peter decoherence Delbrück, Max Descartes, René Deutsch, David Dewar, Katherine Mary Dieks, Dennis diffusion equation Dirac, Paul: appearance and character; in Cambridge; Dirac Equation; Directions in Physics; Dublin colloquium; education; Fermi–Dirac statistics; influence; Nobel Prize; Solvay Congress; transformation theory; view of interpretation; work on quantum mechanics Dirac Equation Directions in Physics (Dirac) DNA Dollfuss, Engelbert Doppler, Johann Christian Doppler effect Dora (cousin) double slit experiment Dublin: Austrian community; Institute for Advanced Studies (DIAS); Schrödinger in; Schrödinger “family life” in; Schrödinger’s arrival; Schrödinger’s departure; Trinity College (TCD); University College Eckart, Carl Eddington, Arthur Edinburgh University Ehrenfest, Paul Einstein, Albert: on “action at a distance”; annus mirabilis; Berlin professorship; Bose–Einstein statistics; Bose’s work; childhood; Congress of Vienna; Cramer’s work; on de Broglie’s work; on double slit experiment; education and career; EPR Paradox; experiences of anti-Semitism; experiences of Nazism; on Feynman’s work; general theory of relativity; influence on Heisenberg’s work; influence on Schrödinger’s work; on Mount Wilson experiment; Nobel Prize; at Princeton; relationship with Schrödinger; on Schrödinger; on Schrödinger’s cat; Solvay Congress; special theory of relativity; on underlying “reality”; view of chance and probability; view of Copenhagen Interpretation; work on Brownian motion; work on light quanta; work on quantum theory of radiation Ekert, Artur electromagnetic oscillators electromagnetism electron(s): Bohr’s work; bond; Born’s work; “collapse of the wave function”; Compton’s work; Copenhagen Interpretation; Copenhagen scientists’ work; de Broglie’s work; Dirac’s work; Einstein’s work; energy; entangled; Fermi–Dirac statistics; Feynman’s work; Heisenberg’s work; interaction between; Lenard’s work; measurement of charge on; Millikan’s work; negative; orbits; pilot wave model; quantum teleportation; quantum “transaction”; radiation resistance; Rutherford’s work; Schrödinger’s work; sharing of; Solvay Congress (1927); spin; “spooky action at a distance”; Thomson’s work; trajectory in cloud chamber; wave equation; waves and particles entanglement: decoherence; experimental confirmation of; FTL signalling; macroscopic; quantum computing; quantum cryptography; quantum teleportation; Rudolph’s work; Schrödinger’s work; term entropy EPR Paradox Epstein, Paul ETH (Eidgenössiche Technische Hochschule), see Zürich Ettinghausen, Andreas Everett, Hugh evolution Exner, Franz Faraday, Michael Farmelo, Graham faster-than-light (FTL) communication (signalling) Fermi, Enrico Fermi–Dirac statistics fermions Feynman, Richard First World War Forster family Fowler, Ralph Franklin, Rosalind Franz Ferdinand, Archduke Franz Josef, Emperor Fraunhofer, Josef von free will Fresnel, Augustin Friedman, Dennis Friedrich Wilhelm III, King of Prussia Frimmel, Franz Galileo Galilei gas in sealed box gases, kinetic theory Geiger, Hans genes: changes in; copying process; Delbrück’s work; DNA; Haldane’s suggestion; molecules; Schrödinger’s work Ghent, University of Gibbs, Willard Gilbert, William Gordon, George Göttingen gravity: Einstein’s work; Newton’s work; Schrödinger’s work Graz: Boltzmann at; Nazism; Schrödinger’s dismissal; Schrödinger’s lectures; Schrödinger’s professorship; Schrödinger’s research “green pamphlet” Greene, Blathnaid Nicolette (Schrödinger’s daughter) Greene, David Habicht, Conrad Habsburg family Haldane, J.

Investment: A History by Norton Reamer, Jesse Downing

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Albert Einstein, algorithmic trading, asset allocation, backtesting, banking crisis, Berlin Wall, Bernie Madoff, Brownian motion, buttonwood tree, California gold rush, capital asset pricing model, Carmen Reinhart, carried interest, colonial rule, credit crunch, Credit Default Swap, Daniel Kahneman / Amos Tversky, debt deflation, discounted cash flows, diversified portfolio, equity premium, estate planning, Eugene Fama: efficient market hypothesis, Fall of the Berlin Wall, family office, Fellow of the Royal Society, financial innovation, fixed income, Gordon Gekko, Henri Poincaré, high net worth, index fund, interest rate swap, invention of the telegraph, James Hargreaves, James Watt: steam engine, joint-stock company, Kenneth Rogoff, labor-force participation, land tenure, London Interbank Offered Rate, Long Term Capital Management, loss aversion, Louis Bachelier, margin call, means of production, Menlo Park, merger arbitrage, moral hazard, mortgage debt, Network effects, new economy, Nick Leeson, Own Your Own Home, pension reform, Ponzi scheme, price mechanism, principal–agent problem, profit maximization, quantitative easing, RAND corporation, random walk, Renaissance Technologies, Richard Thaler, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, Sand Hill Road, Sharpe ratio, short selling, Silicon Valley, South Sea Bubble, sovereign wealth fund, spinning jenny, statistical arbitrage, technology bubble, The Wealth of Nations by Adam Smith, time value of money, too big to fail, transaction costs, underbanked, Vanguard fund, working poor, yield curve

He became quite fluent in finance as a result of this experience, and soon Bachelier found himself back in academia working under the polymath Henri Poincaré.1 He defended the first portion of his thesis, entitled “Theory of Speculation,” in March 1900. In it, he showed how to value complicated French derivatives using advanced mathematics. In fact, his approach bore some similarity to that of Fischer Black and Myron Scholes many years later. Bachelier’s work was the first use of formal models of randomness to describe and evaluate markets. In his paper, Bachelier used a form of what is called Brownian motion.2 Brownian motion was named after Robert Brown, who studied the random motions of pollen in water. Albert Einstein would describe this same phenomenon in one of his famous 1905 papers. The mathematical underpinnings of this description of randomness could be applied not only to the motions of small particles but also to the movements of markets. Bachelier’s work did not seem to have an immediate and profound influence on those markets, however.

Savage wrote postcards to a group of economists asking if any economists were familiar with Bachelier.16 And Samuelson did rethink many of the assumptions Bachelier made, such as noting that the expected return of the speculator should not be zero, as Bachelier suggested, but should rather be positive and commensurate with the risk the speculator is enduring. Otherwise, the investor would simply either not invest or own the risk-free security (short-dated Treasury debt). He also redefined Bachelier’s equations to have the returns in lieu of the actual stock prices move in accordance with a slightly different form of Brownian motion because Bachelier’s form of Brownian motion implied that a stock could potentially have a negative price, which is not sensible, as the concept of limited liability for shareholders implies that the floor of value is zero.17 The Emergence of Investment Theory 235 Samuelson helped motivate the work on derivatives pricing with a 1965 paper on warrants and a 1969 paper with Robert Merton on the same subject—although he did, as he would later note, miss one crucial assumption that Black and Scholes were able to make in their formulation of options prices.18 Samuelson can be considered an intermediary in calling attention to the subfield of derivatives pricing, even if the cornerstone of the most famous final theory was not his own.

See also commercial banks; merchant banks Barbarians at the Gate, 276 Bardi bank, 43–44 Barings Bank, 170–72 behavioral finance, 251–54 bell curve, 239 Benartzi, Shlomo, 252 benchmarking, 328–30 Benedict XIV (pope), 37 Bent, Bruce, 143 Bentham, Jeremy, 36 Index 417 Bergen Tunnel construction project, 178 Berlin Wall, fall of, 96 Bernanke, Ben, 9, 197, 208, 226 beta, 243–45; alpha and, 248–49, 254, 308–9 Bible, 34, 239 Bierman, Harold, 204 bills of exchange, 83–84 Birds, The (Aristophanes), 24 Bismarck, Otto von, 108–9 Black, Fischer, 230, 235–36 BlackRock, 299 Black Thursday (October 24, 1929), 164 Blunt, John, 67–68 Bocchoris, 23 Boesky, Ivan, 147, 181, 184–86 Bogle, Jack, 284–85 bond index funds, 285 bonds: convertible, 178; fabrication of Italian, 163; government, 6, 135, 176; high-yield, 276; holding, 93; investment in, 257, 259, 297, 301; management of, 102 Boness, James, 236 bookkeeping, double-entry, 41 borrower, reputation of, 22–23 Borsa Italiana, 95 Boston, 100 Boston Consulting Group, 194 Boston Post, 157 bourses, 84 Breitowitz, Yitzhok, 150 Bristol-Myers Squibb, 188 Britain: beggar-thy-neighbor policies in, 202; colonial rule of India, 49–50, 61; supplies contract, after American Revolution, 175 British Bankers’ Association, 182 British East India Company, 66, 326 Brookings Institution, 91 Brown, Henry, 143 Brown, Robert, 230 Brownian motion, 230, 234 Brumberg, Richard, 121–22 Brush, Charles, 81 Bubble Act of 1720, 68, 87 bubbles: causes of, 5; housing bubble of 2004–2006, 213–14; South Sea Bubble, 68–69; technology (dot-com bubble of 1999-2000), 187, 213, 223–24, 246, 263, 276, 287 bubonic plague, 75 bucket shops, 90 Buddhist temples, 29–30 budget deficit projections, 218 Buffett, Warren: American Express and, 169; earnings of, 305; on efficient market hypothesis, 250–51; financial leverage and, 6; on real ownership, 4; resource allocation and, 7; as value manager, 140 bullet payments, 321 bull market: in 1920s, 91; of 1990s, 269, 285; after World War II, 92, 143 burghers, 42 Bush, George W., 218, 225 BusinessWeek, 143, 188 Buttonwood Agreement, 88, 97 Byzantines, 52 Cabot, Paul, 141 Cady, Roberts decision, 192 Caesar, 28 Calahan, Edward, 90 California Public Employees Retirement System (CalPERS), 129 418 Investment: A History call option: performance fee as, 310–11; sale of, 151 CalPERS.


pages: 252 words: 73,131

The Inner Lives of Markets: How People Shape Them—And They Shape Us by Tim Sullivan

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Airbnb, airport security, Al Roth, Andrei Shleifer, attribution theory, autonomous vehicles, barriers to entry, Brownian motion, centralized clearinghouse, clean water, conceptual framework, constrained optimization, continuous double auction, deferred acceptance, Donald Trump, Edward Glaeser, experimental subject, first-price auction, framing effect, frictionless, fundamental attribution error, George Akerlof, Goldman Sachs: Vampire Squid, helicopter parent, Internet of things, invisible hand, Isaac Newton, iterative process, Jean Tirole, Jeff Bezos, Johann Wolfgang von Goethe, John Nash: game theory, John von Neumann, Joseph Schumpeter, late fees, linear programming, Lyft, market clearing, market design, market friction, medical residency, multi-sided market, mutually assured destruction, Nash equilibrium, Occupy movement, Peter Thiel, pets.com, pez dispenser, pre–internet, price mechanism, price stability, prisoner's dilemma, profit motive, proxy bid, RAND corporation, ride hailing / ride sharing, Robert Shiller, Robert Shiller, Ronald Coase, school choice, school vouchers, sealed-bid auction, second-price auction, second-price sealed-bid, sharing economy, Silicon Valley, spectrum auction, Steve Jobs, Tacoma Narrows Bridge, technoutopianism, telemarketer, The Market for Lemons, The Wisdom of Crowds, Thomas Malthus, Thorstein Veblen, trade route, transaction costs, two-sided market, uranium enrichment, Vickrey auction, winner-take-all economy

When we looked at that list of papers and thought about what we could do with the information, it occurred to us that these relatively esoteric academic papers had had, like their counterparts in physics, an outsized influence. That seemed worth exploring, not by reprinting the original papers but by examining how those ideas have lived in the world. This half-century’s worth of economic thought—often as incomprehensible to outsiders in its original formulations as Einstein’s investigations into the theory of Brownian motion is to non-physicists—has been used to make markets work better and, in an ever-widening set of applications, has helped them reach more deeply into our lives. The Inner Lives of Markets explores the intersection of those economic ideas and our lives. INTRODUCTION TERMS OF SERVICE At 109 Lincoln Street in Rutland, Vermont, stands a dilapidated yellow clapboard building. Rutland was incorporated in the late nineteenth century, flush with money from the marble quarries just outside town.

His thesis was the beginning of his lifelong project to bring “unification—and clarification—in mathematics” to the profession. Nobel prize winners are generally associated with a particular theory, insight or cohesive set of insights, or even a single specific paper. For Samuelson, rewriting economics in the new language of math was the contribution itself, often borrowing ideas already developed by physicists and mathematicians. He introduced, for example, the idea of Brownian motion (which he borrowed from physics) as a way of understanding financial markets, and a version of Henry-Louis Le Chatelier’s principle (developed by chemists in the nineteenth century) as a tool for understanding market equilibrium. Samuelson didn’t undertake this project alone but was responsible for many of its central contributions. We also see in Samuelson the sense that the discipline imposed by mathematics made economics no less relevant to understanding real-world problems.

INDEX Abidjan, Ivory Coast, 167–168 Adfibs.com, 69 adverse selection, 48, 51–55, 57, 59 advertising, as money burning, 70–71 Super Bowl advertising, 70–71 AdWords, 14, 101 Airbnb, 3, 6, 50, 109, 125, 170–172 Akerlof, George, 43–51, 58–59, 64, 112 Alaskoil experiment, 55–57, 58–59 algebraic topology, 44–45 Amazon, 2, 3, 16, 50, 51, 52, 59, 74, 91, 95, 97, 108, 110, 119, 126, 128–129 American Express, 115–116 America’s Second Harvest, 154–160 Amoroso, Luigi, 21 Angie’s List, 120 “animal spirits,” 50 applied theory in economics, 45, 50, 75–76 Arnold, John, 156–158, 160 Arrow, Kenneth, 30–34, 36–37, 40, 76, 117, 180 ascending price English auctions, 83, 100 asymmetric information, 41, 44–55 attribution theory, 177–178 auctions AdWords, 14, 101 auction theory, 82–84 coat hooks, 151–152, 174 design, 14, 101–102 first-price sealed-bid, 86–87, 99–100 first-price (live), 84 internet, 94–97 types of, 81–82 wireless spectrum, 102–103 See also eBay; Vickrey auctions AuctionWeb, 40 Ausubel, Larry, 98 Azoulay, Pierre, 112 Bank of America, 113–115 barriers to entry, in marketplace, 173 baseball posting system, 79–81 Bazerman, Max, 55–57 Becker, Gary, 35, 161–162 Berman, Eli, 67 Berners-Lee, Tim, 41–42 Big Data, Age of, 15 Blu-ray-HD DVD format war, Sony, 125–126 Book Stacks Unlimited, 42–43 Boston public schools, 144–149 Boston University MBA students experiment (Bazerman and Samuelson), 55–57, 58–59 See also Alaskoil experiment bridge design, 141–142 Brown, William P., 83–84 Brownian motion, 28–29 cab drivers, Uber vs., 169–170, 172 Camp, Garrett, 170 candle auctions, 82 capitalism, free-market, 172–173 car service platform, 169–171 cash-back bonus, 116 cash-for-sludge transactions, 167–169 See also Summers, Larry centralized clearinghouses, 140–141 Champagne fairs, 105–106, 126–128 Changi POW camp, 175–177 Le Chatelier, Henry Louis, 29 Le Chatelier’s principle, 29 cheap talk, 62–66, 69 chess, difference between Cold War and, 26 See also poker, bluffing in child labor, 180 cigarettes, as currency in German POW camp, 8–9 Clarke, Edward, 93 Clavell, James, 175 clerkship offers, with federal judges, 140 coat hook, 151–152, 174 Codes of the Underworld (Gambetta), 68 Cold War, difference between chess and, 26 See also poker, bluffing in Collectible Supplies, 128–129 “College Admissions and the Stability of Marriage” (Gale and Shapley), 137 commitment, signs of, 62–63, 69–71, 72–75 community game, 178–179 competition models of, 35, 166, 172–173 platform, 124–126 unethical conduct with, 180–181 “Competition is for Losers” (Thiel), 173 competitive equilibrium, existence of, 29, 31–34, 36–37, 40, 45, 76 competitive markets, 35, 124–126, 172–174, 180–181 See also platforms competitive signaling, 70–71 congestion pricing model, 86, 94 constrained optimization, 85–86, 133 contractorsfromhell.com, 120 copycat competitors, 172–173 corporate philanthropy, 72–75 Cowles, Alfred, 25, 27 Cowles Commission for Research in Economics, 25, 27, 31, 134 “creative destruction,” 50 credit card platforms, 113–116, 123–124 criminal organizations, informational challenges of, 68 currency, at Stalag VII-A POW camp, 8–9 customer feedback, 52, 74–75 Davis, Harry, 154, 157 Debreu, Gérard, 20, 24, 25, 32–33, 36–37 decentralized match, 139–140 deferred acceptance algorithm, 137–141, 145–149 Delmonico, Frank, 164 descending price auctions, 81–82 design, auction, 14, 101–102 Digital Dealing (Hall), 94 Discover card, 115–116 distribution of income, 22 Domar, Evsey, 36–37 Dorosin, Neil, 142–144 Douglas Aircraft Company, 25 Dow, Bob, 1–2 Dow, Edna, 1–2 Drèze, Jacques, 85–86 dumping toxic waste, transactions for, 167–169 Dutch auctions, 81–82 dysfunction, market, 36, 75–77, 143 eBay adverse selection on, 51–55, 57 auction listings, 94–97 concerns on model for, 43, 46, 48 on seller motivation for giving to charities, 73–75 start of, 39–41 as two-sided market, 109, 119 e-commerce, 41–43, 52–55 “The Economic Organization of a P.O.W.


pages: 855 words: 178,507

The Information: A History, a Theory, a Flood by James Gleick

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Ada Lovelace, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, AltaVista, bank run, bioinformatics, Brownian motion, butterfly effect, citation needed, Claude Shannon: information theory, clockwork universe, computer age, conceptual framework, crowdsourcing, death of newspapers, discovery of DNA, double helix, Douglas Hofstadter, en.wikipedia.org, Eratosthenes, Fellow of the Royal Society, Gödel, Escher, Bach, Henri Poincaré, Honoré de Balzac, index card, informal economy, information retrieval, invention of the printing press, invention of writing, Isaac Newton, Jacquard loom, Jacquard loom, Jaron Lanier, jimmy wales, John von Neumann, Joseph-Marie Jacquard, Louis Daguerre, Marshall McLuhan, Menlo Park, microbiome, Milgram experiment, Network effects, New Journalism, Norbert Wiener, On the Economy of Machinery and Manufactures, PageRank, pattern recognition, phenotype, pre–internet, Ralph Waldo Emerson, RAND corporation, reversible computing, Richard Feynman, Richard Feynman, Simon Singh, Socratic dialogue, Stephen Hawking, Steven Pinker, stochastic process, talking drums, the High Line, The Wisdom of Crowds, transcontinental railway, Turing machine, Turing test, women in the workforce

NORBERT WIENER (1956) (Illustration credit 8.1) He was short and rotund, with heavy glasses and a Mephistophelian goatee. Where Shannon’s fire-control work drilled down to the signal amid the noise, Wiener stayed with the noise: swarming fluctuations in the radar receiver, unpredictable deviations in flight paths. The noise behaved statistically, he understood, like Brownian motion, the “extremely lively and wholly haphazard movement” that van Leeuwenhoek had observed through his microscope in the seventeenth century. Wiener had undertaken a thoroughgoing mathematical treatment of Brownian motion in the 1920s. The very discontinuity appealed to him—not just the particle trajectories but the mathematical functions, too, seemed to misbehave. This was, as he wrote, discrete chaos, a term that would not be well understood for several generations. On the fire-control project, where Shannon made a modest contribution to the Bell Labs team, Wiener and his colleague Julian Bigelow produced a legendary 120-page monograph, classified and known to the several dozen people allowed to see it as the Yellow Peril because of the color of its binder and the difficulty of its treatment.

.… The night was noisier than the day, and at the ghostly hour of midnight, for what strange reasons no one knows, the babel was at its height.♦ But engineers could now see the noise on their oscilloscopes, interfering with and degrading their clean waveforms, and naturally they wanted to measure it, even if there was something quixotic about measuring a nuisance so random and ghostly. There was a way, in fact, and Albert Einstein had shown what it was. In 1905, his finest year, Einstein published a paper on Brownian motion, the random, jittery motion of tiny particles suspended in a fluid. Antony van Leeuwenhoek had discovered it with his early microscope, and the phenomenon was named after Robert Brown, the Scottish botanist who studied it carefully in 1827: first pollen in water, then soot and powdered rock. Brown convinced himself that these particles were not alive—they were not animalcules—yet they would not sit still.

This idea is carried still further in certain commercial codes where common words and phrases are represented by four- or five-letter code groups with a considerable saving in average time. The standardized greeting and anniversary telegrams now in use extend this to the point of encoding a sentence or two into a relatively short sequence of numbers.♦ To illuminate the structure of the message Shannon turned to some methodology and language from the physics of stochastic processes, from Brownian motion to stellar dynamics. (He cited a landmark 1943 paper by the astrophysicist Subrahmanyan Chandrasekhar in Reviews of Modern Physics.♦) A stochastic process is neither deterministic (the next event can be calculated with certainty) nor random (the next event is totally free). It is governed by a set of probabilities. Each event has a probability that depends on the state of the system and perhaps also on its previous history.


pages: 240 words: 60,660

Models. Behaving. Badly.: Why Confusing Illusion With Reality Can Lead to Disaster, on Wall Street and in Life by Emanuel Derman

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Albert Einstein, Asian financial crisis, Augustin-Louis Cauchy, Black-Scholes formula, British Empire, Brownian motion, capital asset pricing model, Cepheid variable, crony capitalism, diversified portfolio, Douglas Hofstadter, Emanuel Derman, Eugene Fama: efficient market hypothesis, Henri Poincaré, Isaac Newton, law of one price, Mikhail Gorbachev, quantitative trading / quantitative finance, random walk, Richard Feynman, Richard Feynman, riskless arbitrage, savings glut, Schrödinger's Cat, Sharpe ratio, stochastic volatility, the scientific method, washing machines reduced drudgery, yield curve

I showed that expected return is proportional to risk by using just two principles: (1) you should expect equal returns from equal risks, and (2) a stock’s risk is solely the volatility of the diffusion illustrated in Figure 5.3. The first principle is pure theory and hard to argue with: If two securities truly have the same risk, how could you not expect the same return from them? But that’s an expectation. In life, expectations aren’t necessarily fulfilled. The second assumption is pure model. The EMM’s picture of price movements goes by several names: a random walk, diffusion, and Brownian motion. One of its origins is in the description of the drift of pollen particles through a liquid as they collide with its molecules. Einstein used the diffusion model to successfully predict the square root of the average distance the pollen particles move through the liquid as a function of temperature and time, thus lending credence to the existence of hypothetical molecules and atoms too small to be seen.

See evil bailouts bare electrons Barfield, Owen Bedazzled (film) Begin, Menachem behavior, human: adequate knowledge and EMM as assumption about explanations for and humans as responsible for their actions and idolatry of models Law of One Price and laws of pragmamorphism and Ben-Gurion, David Bernoulli, Daniel Bernstein, Jeremy beta: CAPM and Betar (Brit Yosef Trumpeldor) binocular diplopia birds Black, Fischer Black-Scholes Model Merton and Blake, William Bnei Akiva (Sons of Akiva) Bnei Zion (Sons of Zion) body-mind relationship Bohr, Aage Bohr, Niels bonds: financial models and See also type of bond Boyle’s Law Brahe, Tycho brain Brave New World (Huxley) Brownian motion bundling of complex products cage: moth in perfect calibration Cape Flats Development Association (South Africa) Capital Asset Pricing Model (CAPM) capitalism caricatures: models as cash. See currency/cash Cauchy, Augustin-Louis causes Cepheid variable stars chalazion chaver (comrade) Chekhov, Anton chemistry: electromagnetic theory and Chesterton, G. K. Chinese choice chromatography Churchill, Winston Coetzee, J.

The Singularity Is Near: When Humans Transcend Biology by Ray Kurzweil

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additive manufacturing, AI winter, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, anthropic principle, Any sufficiently advanced technology is indistinguishable from magic, artificial general intelligence, augmented reality, autonomous vehicles, Benoit Mandelbrot, Bill Joy: nanobots, bioinformatics, brain emulation, Brewster Kahle, Brownian motion, business intelligence, c2.com, call centre, carbon-based life, cellular automata, Claude Shannon: information theory, complexity theory, conceptual framework, Conway's Game of Life, cosmological constant, cosmological principle, cuban missile crisis, data acquisition, Dava Sobel, David Brooks, Dean Kamen, disintermediation, double helix, Douglas Hofstadter, en.wikipedia.org, epigenetics, factory automation, friendly AI, George Gilder, Gödel, Escher, Bach, informal economy, information retrieval, invention of the telephone, invention of the telescope, invention of writing, Isaac Newton, iterative process, Jaron Lanier, Jeff Bezos, job automation, job satisfaction, John von Neumann, Kevin Kelly, Law of Accelerating Returns, life extension, linked data, Loebner Prize, Louis Pasteur, mandelbrot fractal, Mikhail Gorbachev, mouse model, Murray Gell-Mann, mutually assured destruction, natural language processing, Network effects, new economy, Norbert Wiener, oil shale / tar sands, optical character recognition, pattern recognition, phenotype, premature optimization, randomized controlled trial, Ray Kurzweil, remote working, reversible computing, Richard Feynman, Richard Feynman, Rodney Brooks, Search for Extraterrestrial Intelligence, semantic web, Silicon Valley, Singularitarianism, speech recognition, statistical model, stem cell, Stephen Hawking, Stewart Brand, strong AI, superintelligent machines, technological singularity, Ted Kaczynski, telepresence, The Coming Technological Singularity, transaction costs, Turing machine, Turing test, Vernor Vinge, Y2K, Yogi Berra

.: Landes Bioscience, 1999), pp. 309–12, http://www.nanomedicine.com/NMI/9.4.2.5.htm. 154. George Whitesides, "Nanoinspiration: The Once and Future Nanomachine," Scientific American 285.3 (September 16,2001): 78–83. 155. "According to Einstein's approximation for Brownian motion, after 1 second has elapsed at room temperature a fluidic water molecule has, on average, diffused a distance of ~50 microns (~400,000 molecular diameters) whereas a l-rnicron nanorobot immersed in that same fluid has displaced by only ~0.7 microns (only ~0.7 device diameter) during the same time period. Thus Brownian motion is at most a minor source of navigational error for motile medical nanorobots," See K. Eric Drexler et al., "Many Future Nanomachines: A Rebuttal to Whitesides' Assertion That Mechanical Molecular Assemblers Are Not Workable and Not a Concern," a Debate about Assemblers, Institute for Molecular Manufacturing, 2001, http://www.imm.org/SciAmDebate2/whitesides.html. 156.

George Whitesides complained in Scientific American that "for nanoscale objects, even if one could fabricate a propeller, a new and serious problem would emerge: random jarring by water molecules. These water molecules would be smaller than a nanosubmarine but not much smaller."154 Whitesides's analysis is based on misconceptions. All medical nanobot designs, including those of Freitas, are at least ten thousand times larger than a water molecule. Analyses by Freitas and others show the impact of the Brownian motion of adjacent molecules to be insignificant. Indeed, nanoscale medical robots will be thousands of times more stable and precise than blood cells or bacteria.155 It should also be pointed out that medical nanobots will not require much of the extensive overhead biological cells need to maintain metabolic processes such as digestion and respiration. Nor do they need to support biological reproductive systems.

It's simple enough, but consider the diverse and beautiful ways it manifests itself: the endlessly varying patterns as it cascades past rocks in a stream, then surges chaotically down a waterfall (all viewable from my office window, incidentally); the billowing patterns of clouds in the sky; the arrangement of snow on a mountain; the satisfying design of a single snowflake. Or consider Einstein's description of the entangled order and disorder in a glass of water (that is, his thesis on Brownian motion). Or elsewhere in the biological world, consider the intricate dance of spirals of DNA during mitosis. How about the loveliness of a tree as it bends in the wind and its leaves churn in a tangled dance? Or the bustling world we see in a microscope? There's transcendence everywhere. A comment on the word "transcendence" is in order here. "To transcend" means "to go beyond," but this need not compel us to adopt an ornate dualist view that regards transcendent levels of reality (such as the spiritual level) to be not of this world.


pages: 291 words: 81,703

Average Is Over: Powering America Beyond the Age of the Great Stagnation by Tyler Cowen

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Amazon Mechanical Turk, Black Swan, brain emulation, Brownian motion, Cass Sunstein, choice architecture, complexity theory, computer age, computer vision, cosmological constant, crowdsourcing, dark matter, David Brooks, David Ricardo: comparative advantage, deliberate practice, Drosophila, en.wikipedia.org, endowment effect, epigenetics, Erik Brynjolfsson, eurozone crisis, experimental economics, Flynn Effect, Freestyle chess, full employment, future of work, game design, income inequality, industrial robot, informal economy, Isaac Newton, Khan Academy, labor-force participation, Loebner Prize, low skilled workers, manufacturing employment, Mark Zuckerberg, meta analysis, meta-analysis, microcredit, Narrative Science, Netflix Prize, Nicholas Carr, pattern recognition, Peter Thiel, randomized controlled trial, Ray Kurzweil, reshoring, Richard Florida, Richard Thaler, Ronald Reagan, Silicon Valley, Skype, statistical model, stem cell, Steve Jobs, Turing test, Tyler Cowen: Great Stagnation, upwardly mobile, Yogi Berra

Larry Kaufman, who developed the evaluation function for the Rybka program, and who is the mastermind of the Komodo program, graduated from MIT with an undergraduate degree in economics in 1968. He went to work on Wall Street as a broker and soon started developing his own form of options-pricing theory, working independently of Fischer Black and Myron Scholes; Scholes later won a Nobel Prize for that contribution. Kaufman’s theory was based on ideas of Brownian motion and the logistic function, the latter of which he took from formulas for calculating chess ratings. In the 1970s he made money by applying his options-pricing work through a trading firm and stopped when the profits went away, and he has since dedicated his life to chess and computer chess, including his work on Rybka and Komodo. He lives in a fine house in one of the nicest parts of suburban Maryland, with his beautiful wife and young daughter.

., 37, 164 Babbage, Charles, 6 Banerjee, Abhijit, 222 BBC, 144 Becker, Gary, 226–27 behavioral economics, 75–76, 99, 105, 110, 149, 227 Belle (chess program), 46 benefit costs, 36, 59, 113 Benjamin, Joel, 47 Berlin, Germany, 246 Berra, Yogi, 229 biases, cognitive, 99–100 Bierce, Ambrose, 134 “Big Data,” 185, 221 Black, Fischer, 203 blogs, 180–81 Bonaparte, Napoleon, 148 Borjas, George, 162 “bots,” 144–45 “brain emulation,” 137–38. See also artificial intelligence (AI) branes, 214 Brazil, 20 Breedlove, Philip M., 20 Bresnahan, Timothy F., 33 Brookings Institution, 53 Brooklyn, New York, 172, 240 Brownian motion, 203 Brynjolfsson, Erik, 6, 33 Burks, John, 62 business cycles, 45 business negotiations, 73, 158 California, 8, 241 Campbell, Howard, 246 Canada, 20, 171, 177 Candidates Match, 156 Capablanca, Jose Raoul, 150 capital flows, 166 capitalism, 258 careers, 41–44, 119–25, 126, 202 Carlsen, Magnus, 104, 156, 189 Carr, Nicholas, 153–54 Caterpillar, 38 cell phone service, 118 CEOs, 100 Chen, Yingheng, 79 chess and cheating, 146–51 Chess Olympiad, 147, 189 computer’s influence on quality of play, 106–8 and decision making, 98–99, 101–2, 104–5, 129 early computer chess, 7, 46–47, 67–70 and face-to-face instruction, 195 and gender issues, 31, 106–8 and globalization of competition, 168 and intuition, 68–70, 72, 97, 99, 101, 105–6, 109–10, 114–15 machine and human styles contrasted, 75–76, 77–86 machine vs. machine matches, 70–75 as model for education, 185–88, 191–92, 202–3 and opening books, 83–85, 86–87, 107, 135, 203 and player ratings, 120 simplicity of rules, 48–49 spectator interest in, 156–57 See also Freestyle chess Chess Tiger (chess program), 78 children and wealth inequality, 249 China chess players from, 108, 189 and demographic trends, 230 and geographic trends, 177 and global competition, 171 and labor competition, 5, 163–64, 167, 169–70 and political trends, 252 and scientific specialization, 216 choice.


pages: 634 words: 185,116

From eternity to here: the quest for the ultimate theory of time by Sean M. Carroll

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Albert Einstein, Albert Michelson, anthropic principle, Arthur Eddington, Brownian motion, cellular automata, Claude Shannon: information theory, Columbine, cosmic microwave background, cosmological constant, cosmological principle, dark matter, dematerialisation, double helix, en.wikipedia.org, gravity well, Harlow Shapley and Heber Curtis, Henri Poincaré, Isaac Newton, John von Neumann, Lao Tzu, lone genius, New Journalism, Norbert Wiener, pets.com, Richard Feynman, Richard Feynman, Richard Stallman, Schrödinger's Cat, Slavoj Žižek, Stephen Hawking, stochastic process, the scientific method, wikimedia commons

This was problematic, as the Temperance movement was strong in America at the time, and Berkeley in particular was completely dry; a recurring theme in Boltzmann’s account is his attempts to smuggle wine into various forbidden places.193 We will probably never know what mixture of failing health, depression, and scientific controversy contributed to his ultimate act. On the question of the existence of atoms and their utility in understanding the properties of macroscopic objects, any lingering doubts that Boltzmann was right were rapidly dissipating when he died. One of Albert Einstein’s papers in his “miraculous year” of 1905 was an explanation of Brownian motion (the seemingly random motion of small particles suspended in air) in terms of collisions with individual atoms; most remaining skepticism on the part of physicists was soon swept away. Questions about the nature of entropy and the Second Law remain with us, of course. When it comes to explaining the low entropy of our early universe, we won’t ever be able to say, “Boltzmann was right,” because he suggested a number of different possibilities without ever settling on one in particular.

TIME IS PERSONAL 53 On the other hand, the achievements for which Paris Hilton is famous are also pretty mysterious. 54 Einstein’s “miraculous year” was 1905, when he published a handful of papers that individually would have capped the career of almost any other scientist: the definitive formulation of special relativity, the explanation of the photoelectric effect (implying the existence of photons and laying the groundwork for quantum mechanics), proposing a theory of Brownian motion in terms of random collisions at the atomic level, and uncovering the equivalence between mass and energy. For most of the next decade he concentrated on the theory of gravity; his ultimate answer, the general theory of relativity, was completed in 1915, when Einstein was thirty-six years old. He died in 1955 at the age of seventy-six. 55 We should also mention Dutch physicist Hendrik Antoon Lorentz, who beginning in 1892 developed the idea that times and distances were affected when objects moved near the speed of light, and derived the “Lorentz transformations,” relating measurements obtained by observers moving with respect to each other.

See also event horizons; singularities and arrow of time and baby universes model and closed timelike curves and entropy evaporation of and growth of structure and Hawking radiation and holographic principle and information and Laplace and particle accelerators and quantum tunneling and quasars and the real world and redshift and spacetime and string theory thermodynamic analogy and uncertainty principle uniformity of The Black Hole Wars (Susskind) block time/block universe perspective Bohr, Niels Boltzmann, Emma Boltzmann, Ludwig and anthropic principle and arrow of time and atomic theory and black holes death and de Sitter space and entropy and the H-Theorem and initial conditions of the universe and kinetic theory and Loschmidt’s reversibility objection and Past Hypothesis and Principle of Indifference and recurrence theorem and the Second Law of Thermodynamics and statistical mechanics Boltzmann brains Boltzmann-Lucretius scenario Bondi, Hermann boost. bosons bouncing-universe cosmology boundary conditions and cause and effect described and initial conditions of the universe and irreversibility and Maxwell’s Demon and recurrence theorem and time symmetry Bousso, Raphael Brahe, Tycho branes Brillouinéon brown dwarfs Brownian motion Bruno, Giordano bubbles of vacuum Buddhism Bureau of Longitude Callender, Craig Callisto caloric Calvin, John Calvino, Italo Carnot, Lazare Carnot, Nicolas Léonard Sadi Carrey, Jim Carroll, Lewis cause and effect celestial mechanics cellular automata CERN C-field Chandrasekhar Limit chaotic dynamics The Character of Physical Law (Feynman) charge charge conjugation checkerboard world exercise and arrow of time background of and conservation of information and Hawking radiation and holographic principle and information loss and interaction effects and irreversibility and Principle of Indifference and symmetry and testing hypotheses chemistry Chen, Jennifer choice Chronology Protection Conjecture circles in time.


pages: 654 words: 204,260

A Short History of Nearly Everything by Bill Bryson

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Albert Einstein, Albert Michelson, Alfred Russel Wallace, All science is either physics or stamp collecting, Arthur Eddington, Barry Marshall: ulcers, Brownian motion, California gold rush, Cepheid variable, clean water, Copley Medal, cosmological constant, dark matter, Dava Sobel, David Attenborough, double helix, Drosophila, Edmond Halley, Ernest Rutherford, Fellow of the Royal Society, Harvard Computers: women astronomers, Isaac Newton, James Watt: steam engine, John Harrison: Longitude, Kevin Kelly, Kuiper Belt, Louis Pasteur, luminiferous ether, Magellanic Cloud, Menlo Park, Murray Gell-Mann, out of africa, Richard Feynman, Richard Feynman, Stephen Hawking, supervolcano, Thomas Malthus, Wilhelm Olbers

Partly it was to do with the limitations of equipment—there were, for instance, no centrifuges until the second half of the century, severely restricting many kinds of experiments—and partly it was social. Chemistry was, generally speaking, a science for businesspeople, for those who worked with coal and potash and dyes, and not gentlemen, who tended to be drawn to geology, natural history, and physics. (This was slightly less true in continental Europe than in Britain, but only slightly.) It is perhaps telling that one of the most important observations of the century, Brownian motion, which established the active nature of molecules, was made not by a chemist but by a Scottish botanist, Robert Brown. (What Brown noticed, in 1827, was that tiny grains of pollen suspended in water remained indefinitely in motion no matter how long he gave them to settle. The cause of this perpetual motion—namely the actions of invisible molecules—was long a mystery.) Things might have been worse had it not been for a splendidly improbable character named Count von Rumford, who, despite the grandeur of his title, began life in Woburn, Massachusetts, in 1753 as plain Benjamin Thompson.

(An application to be promoted to technical examiner second class had recently been rejected.) His name was Albert Einstein, and in that one eventful year he submitted to Annalen der Physik five papers, of which three, according to C. P. Snow, “were among the greatest in the history of physics”—one examining the photoelectric effect by means of Planck's new quantum theory, one on the behavior of small particles in suspension (what is known as Brownian motion), and one outlining a special theory of relativity. The first won its author a Nobel Prize and explained the nature of light (and also helped to make television possible, among other things).*17 The second provided proof that atoms do indeed exist—a fact that had, surprisingly, been in some dispute. The third merely changed the world. Einstein was born in Ulm, in southern Germany, in 1879, but grew up in Munich.

“Atoms cannot be perceived by the senses . . . they are things of thought,” he wrote. The existence of atoms was so doubtfully held in the German-speaking world in particular that it was said to have played a part in the suicide of the great theoretical physicist, and atomic enthusiast, Ludwig Boltzmann in 1906. It was Einstein who provided the first incontrovertible evidence of atoms' existence with his paper on Brownian motion in 1905, but this attracted little attention and in any case Einstein was soon to become consumed with his work on general relativity. So the first real hero of the atomic age, if not the first personage on the scene, was Ernest Rutherford. Rutherford was born in 1871 in the “back blocks” of New Zealand to parents who had emigrated from Scotland to raise a little flax and a lot of children (to paraphrase Steven Weinberg).


pages: 389 words: 109,207

Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street by William Poundstone

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Albert Einstein, anti-communist, asset allocation, Benoit Mandelbrot, Black-Scholes formula, Brownian motion, buy low sell high, capital asset pricing model, Claude Shannon: information theory, computer age, correlation coefficient, diversified portfolio, en.wikipedia.org, Eugene Fama: efficient market hypothesis, high net worth, index fund, interest rate swap, Isaac Newton, Johann Wolfgang von Goethe, John von Neumann, Long Term Capital Management, Louis Bachelier, margin call, market bubble, market fundamentalism, Marshall McLuhan, New Journalism, Norbert Wiener, offshore financial centre, publish or perish, quantitative trading / quantitative finance, random walk, risk tolerance, risk-adjusted returns, Robert Shiller, Robert Shiller, Ronald Reagan, short selling, speech recognition, statistical arbitrage, The Predators' Ball, The Wealth of Nations by Adam Smith, transaction costs, traveling salesman, value at risk, zero-coupon bond

As we’ve already seen, the fluctuations of a bettor’s bankroll in a game of chance constitute a random walk (a one-dimensional random walk, since wealth can only move up or down). With time, the gambler’s wealth strays further and further from its original value, and this eventually leads to ruin. At about the time Bachelier was writing, Albert Einstein was puzzling over Brownian motion, the random jitter of microscopic particles suspended in a fluid. The explanation, Einstein surmised, was that the particles were being hit on all sides by invisible molecules. These random collisions cause the visible motion. The mathematical treatment of Brownian motion that Einstein published in 1905 was similar to, but less advanced than, the one that Bachelier had already derived for stock prices. Einstein, like practically everyone else, had never heard of Bachelier. The Random Walk Cosa Nostra SAMUELSON ADOPTED Bachelier’s ideas into his own thinking.


pages: 153 words: 12,501

Mathematics for Economics and Finance by Michael Harrison, Patrick Waldron

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Brownian motion, buy low sell high, capital asset pricing model, compound rate of return, discrete time, incomplete markets, law of one price, market clearing, risk tolerance, riskless arbitrage, short selling, stochastic process

It follows very naturally from the stuff in Section 5.4. 7.2.2 The Black-Scholes option pricing model Fischer Black died in 1995. In 1997, Myron Scholes and Robert Merton were awarded the Nobel Prize in Economics ‘for a new method to determine the value of derivatives.’ See http://www.nobel.se/announcement-97/economy97.html Black and Scholes considered a world in which there are three assets: a stock, whose price, S̃t , follows the stochastic differential equation: dS̃t = µS̃t dt + σ S̃t dz̃t , where {z̃t }Tt=0 is a Brownian motion process; a bond, whose price, Bt , follows the differential equation: dBt = rBt dt; and a call option on the stock with strike price X and maturity date T . Revised: December 2, 1998 138 7.2. ARBITRAGE AND PRICING DERIVATIVE SECURITIES They showed how to construct an instantaneously riskless portfolio of stocks and options, and hence, assuming that the principle of no arbitrage holds, derived the Black-Scholes partial differential equation which must be satisfied by the option price.


pages: 119 words: 10,356

Topics in Market Microstructure by Ilija I. Zovko

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Brownian motion, continuous double auction, correlation coefficient, financial intermediation, Gini coefficient, market design, market friction, market microstructure, Murray Gell-Mann, p-value, quantitative trading / quantitative finance, random walk, stochastic process, stochastic volatility, transaction costs

Models of spread, starting withDemsetz (1968); Tinic (1972); Stoll (1978); Amihud and Mendelson (1980); Ho and Stoll (1981), have examined the possible determinants of spreads as a result of rational, utilitymaximizing problem faced by the market makers. Models providing insight into the utility-maximizing response of agents to other various measures of market conditions such as volatility are for example Lo (2002) who investigate a simple model in which the log stock price is modeled as a Brownian motion diffusion process. Provided agents prefer a lower expected execution time, their model predicts a positive relationship between volatility and limit order placement. Copeland and Galai (1983); Glosten and Milgrom (1985); Easley and O’Hara (1987); Glosten (1995); Foucault (1999); Easley et al. (2001) examine asymmetric information effects on order placement. Andersen (1996) modifies the Glosten and Milgrom (1985) model with the stochastic volatility and information flow perspective.


pages: 1,079 words: 321,718

Surfaces and Essences by Douglas Hofstadter, Emmanuel Sander

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affirmative action, Albert Einstein, Arthur Eddington, Benoit Mandelbrot, Brownian motion, Chance favours the prepared mind, cognitive dissonance, computer age, computer vision, dematerialisation, Donald Trump, Douglas Hofstadter, Ernest Rutherford, experimental subject, Flynn Effect, Georg Cantor, Gerolamo Cardano, Golden Gate Park, haute couture, haute cuisine, Henri Poincaré, Isaac Newton, l'esprit de l'escalier, Louis Pasteur, Mahatma Gandhi, mandelbrot fractal, Menlo Park, Norbert Wiener, place-making, Silicon Valley, statistical model, Steve Jobs, Steve Wozniak, theory of mind, upwardly mobile, urban sprawl

One other factor that might have contributed to Einstein’s faith in his analogy between the physics of the ideal gas and that of the black body (not just between the mathematical formulas for their spectra) was the fact that only a few months earlier, he had found and deeply exploited an analogy between an ideal gas and another physical system — namely, a liquid containing colloidal particles whose nonstop, apparently random hopping-about could be observed through a microscope. This analogy had allowed him to argue persuasively for the existence of extremely tiny invisible molecules that were incessantly pelting the far larger colloidal particles (like thousands of gnats bashing randomly into hanging lamps) and giving them their mysterious hops, known as “Brownian motion”. It is thus probable that two distinct forces in Einstein’s mind — the mathematical similarity of the formulas and also his recent Brownian-motion analogy — gave him great trust in his analogy between a black body and an ideal gas. In any case, building on the bedrock of his latest analogy, Einstein undertook a series of computations, all based on thermodynamics, the branch of physics that he thought of as the deepest and most reliable of all. First he calculated the entropy of each of the systems and then he transformed the two entropy formulas so that they would look as similar as possible to each other; in fact, at the end of his ingenious manipulations, they wound up exactly identical except for the algebraic form of one simple exponent.

INDEX —A— “A”, diversity of members of the category, 4–5, 57; picture, 5 “a”: as naming a category, 76; as vowel recognized in speech without one’s knowing how, 511, 512 “A rolling stone gathers no moss”, opposite interpretations of, 102 Aaron, Henry, 325–326 abc ⇒ abd, see Copycat analogies Abel, Niels Henrik, 446 abstract dog and abstract bite, 104 abstract, grounded in the concrete, 28–29, 286–289, 333–337 abstraction: absurd levels of, 107–108, 166, 354, 448–449; as central to expertise, 245–246; by children, 38, 42–43; defined, 187; drive towards, 288; going hand-in-hand with generalization in math, 449; hierarchies of, 235–246; as impoverishing and enriching, 250; as key to encoding, 172, 174–176; legitimized by physics, 448; as luxury add-on to embodied cognition, 288–289; moving between levels of, 30–31; nature of, 107; opaque legalese as bad form of, see legalese; optimal level of, 108; relentless push towards, in mathematics, 448; streamlined by preplaced pitons, 131; techniques for, in mathematics, 449; unconscious acts of, 150–152, 165–166; in word problems in math, 428; see also category extension accelerating frames of reference, 486, 488 acceleration: as indistinguishable from gravity, 491–492, 493–494, 496; linear versus circular, 497 acronyms, 89–93; catchiness of, 90; early examples of, 89–90; efficiency of, 92; list of, 90–91 actable-upon objects, category of, 253 action errors, caused by analogies, 279–280, 404–407 activated categories seeking instances of themselves, 299 adaptation of word meanings to contexts, 196–198 address, generalization to virtual world, 385–386, 395, 398 ad-hoc categories, 137–138; in metaphor understanding, 228–229, 232 adjectives: as labels for the two types of mass, 485; as names of categories, 272 Æsop, 112, 115, 388 affordances, perceptual, 278, 345, 450 airlines and airports as parts of hub concept, 52 airplanes, undetectabilityof motion of, 466–467 airport scenes: evoking words left and right, 33–34; evoking memories of analogous scenes, 157–158; as transculturation of métro scene, 377–379 Alberic of Monte Cassino, 22 Albert Einstein, Creator and Rebel, 473; see also Banesh Hoffmann Albert’s Auberge, excellent coffee of, 462 algebra of classical categories, 56 Alice in Many Tongues (Weaver), 369–370, 372 alignment of two lives on time axis, 433–434 allegory for strange versus normal mass, 476 ambiguous category-membership, 59, 189–192 America/China frame blend, 367–368 amplification, proverbs about, 109 analogic versus logic, 258, 307–310, 311–312, 338, 393, 410, 439, 452, 453, 474, 499–500, 501; see also esthetics analogical fabric of thought, 127 analogical reasoning, mistaken for analogy’s essence, 16–17, 283 analogies: between analogies, 27, 211–212, 502; between random things, 302; as bridges between mental entities, 181–184; coercing one’s flow of thought, 257, 258, 310–313, 444; as cognitive luxuries, 506; in competition, 260–278, 333; conveying truth despite falsity, 366; to counterfactual situations, 362; deep versus shallow, 337–346, 351–357, 375–376, 454–455, 517; as discardable crutches, 392, 421; down-to-earth, great utility of, 23, 507, 509, 516; by Einstein turning out to be eternal truths, 453–454, 486; engendered by obsessions, 258, 299–305, 524; extremely bland cases of, 155–156, 281–284, 507–509; failure of one as stepping stone en route to a deeper one, 356–357, 481, 490–491; as fallible and misleading, 22–24, 435; formal versus physical, 458; as frilly baubles and bangles, 506; functional and visual, coordinated, 277–278; as gems, 16, 506; high frequency of, 18, 507–510; as icing on cognition’s cake, 506, 508; imposing themselves, 29, 31, 289–307, 310–314; inspired by previous analogies, 211–212; invading minds willy-nilly, 257; involving frame-blending, 359–367; involving grammar patterns, 69–70; irrepressibility of, 104, 155, 157, 297, 305–313, 513–514; jumping unbidden to mind, 513–514; latent in semantic halos, 49, 271; like asparagus tips, 135; at the low end of the creativity spectrum, 450; manipulated by us, 331, 382–383, 513; manipulating our thoughts, 29, 31, 315, 331, 382–383, 501, 514; as mere sparkle and pizzazz, 506; as misleading, 21–23; mundane, by Albert Einstein, 454–455; nonstop deluge of, 155; not necessarily a source of pride, 517; objectivity of, 181–183; partially correct and partially wrong, 361; power of, 331–332, 444; pressures pushing for, 300–301, 355–356, 458; purposeless, 258, 281–286; rarity of, 506; seen as analogous to wild horses, 392; as sources of speech and action errors, 259–280; spicy one-line examples, list of, 136; stereotypes of, 135–136, 392, 486; strength of, as reflecting number of resemblances, 516; as strokes of genius, 16–17; superficial, in machine translation, 373, 375; taboo cases of, 104; as training wheels, 392; trivial and meaningless, ceaseless production of, 282, 284–286; unconscious, 259–281, 282, 285–286, 383, 386, 390, 403–407, 514; as uninvited guests, 31, 257; used in thermodynamics but not in electrodynamics, 337; versus frame blends, 363–364, 366–367; visual and sensory, 277–278, 286–289; wild and implausible, as hypothetical crux of creativity, 452 analogues versus schemas, 336–337 analogy: as analogous to asparagus tips, 135; as analogous to siren songs, 23; as analogous to wild horses, 392 analogy leapfrog, 211–212 analogy-making: addictive nature of, 155; as applying to entities versus applying to relations, 517–519; automaticity of, 513–514; as bridge-building between two items on the same level, 519–522; as a cognitive luxury, 506; as compatible with very few disparities, 515–517; as a conscious process, 510–513; as contrasted with assignment to a schema, 336; as the core of cognition, 3, 18, 25–26, 383, 505, 530; as creative, 508–510; as the crux of intelligence, 127; in decision-making, 330–337; as the Delaware of cognition, 17; delight provided by, 506; dependence on familiarity of source domain, 339–340; described by experts exactly as categorization is described, 436, 506; driven by surface-level cues, 337–346; efficiency of, 346; embodiment and, 287–289; in everyday life versus in wartime, 333–335; evoking symbol-manipulation recipes in mathematics, 450–451; as fallible and misleading, 22–24, 435, 527–529; as formal reasoning, 16; frame-blending and, 357–367; as the fuel and fire of thinking, 3; in getting used to new mathematical concepts, 442–444; going as deep as one can go in, 360; as the heartbeat of thought, 15, 17; identity with categorization, 503–530; illusion of necessary seriousness of, 282; incessant avalanche of, 18, 24, 28; as jumping between two levels of abstraction, 519–522; lack of right answers in, 16, 350, 352; as lacking in computers, 25; as the machinery of categorization, 15, 17, 39–49, 183–184, 309, 336, 399; as making the novel familiar, 436, 506; as making the world predictable, 436; by mathematicians, 439–451; as mediating object recognition, 19; misleading stereotypes of, 15–17; in mundane mathematical manipulations, 449–450; naïve analogy concerning, 451; as noble, 508; not used in domestic politics, 337; as objective, 522–526; opacity of the mechanisms of, 511; at the origin of metaphors, 63–64; in poetry translation, 380–381; as prerequisite to survival, 155, 157; as primarily done in intelligence tests, 16; as a rare luxury, 505–508; in real life as opposed to the lab, 339; as reliable, 527–529; as risky, 527; as routine, 508–510; in scientific discovery, 32, 210–214, 361; as subjective, 522–526; supposedly driven by superficial features only, 337–340; supposedly strengthened by disparities, 515–517; as suspect, 527–529; in translation of this book, 377–382; ubiquity of, 506–508; as an unconscious process, 510–513; underlying all word choices, see word choices; utility of, 135; versus categorization, 434–437; as a voluntary process, 513–514; in wartime decision-making, 17, 331–337; wide range of, 19; wide spectrum of abstraction of, in mathematics, 451 “analogy”, rarity of the word, 135 and-situations as a category, 55, 70–75; contrasted with but-situations, 72–75 Anderson, John, 436 angel stung by bumblebee, see interplanetary bumblebee animal, as highly variegated category, 516 animal words as metaphors, 228–232 animals: conceptual repertoires of, 54; as Platonic categories, 56 Ann, as member of many categories, 59, 190, 191 Anna, as spokesperson for the centrality of analogy-making, 503–529; poofing into thin air, 529; see also Katy, Katyanna annihilating nano-boulders, 482 annus minimus of Ellen Ellenbogen, 463–464 annus mirabilis of Albert Einstein, 453, 467, 468–469 “Ant and the Grasshopper” (Æsop), 388 anti-economy, principle of, as a consequence of the dominance of the superficial in reminding, 341 ants: near Grand Canyon, see Danny at Grand Canyon; on orange, watching eclipse, 204–205, 367 appearances, as deceptive versus revelatory, 345 Arabic language, proverb in, 106 Archimedes, 130, 250–252, 300–301, 509; of minigolf, the, 222 Argentina, role of, in Falkland Islands War, 332 Aristotle, 15–16, 21, 437; of the airwaves, the, 222 arithmetical operations, relative difficulty of, 425 “Arizona Ants” (Kellie Gutman), 160, 380–381 army/thought analogy, 26, 27 Arnaud, Pierre, 259 Ars Magna (Cardano), 438–439 articles (“a” and “the”), as names of categories, 76 artificial intelligence, 20, 25 artistic unity, as goal of Einstein, 477, 495; see also esthetics “as deep as one can go”, in analogy-making, 360 asparagus tip analogies, 19 “atmospheric harbor” as incomprehensible phrase, 86 “atom” as an unsplittable etym in English, 89 atom/solar system analogy, 142–143, 510, 513, 515, 518 atoms: lingering doubts about existence of, 459, 475, 487; vibrating in solids to make heat, 461, 475; vibrating in wall of black body, 456 attic, concept of 48–49, 278 avoidance maneuvers while walking, analogy-making in, 285 —B— Babbage, Charles, 369 Bach, Johann Sebastian, 312; of the vibraphone, the, 222; rapid essence-spotting by, 501; Bachelard, Gaston, 22 bagels belonging to a single batch, 309–310, 529 bait-and-switch as a concept available to anglophones, 123–124 balls, bells, and bowls, 488 Banach, Stefan, 502 banalogies (banal analogies), 143–156, 281–286; certainty of, 529; by Einstein, 454–455; elusiveness of, due to blandness, 152, 282, 285–286; great utility of, 23, 507, 509, 516, 529 bananalogy, of use when seeking bananas, 156 “band”, diverse meanings of, 3–4 Bar-Hillel, Yehoshua, 370 bark worse than bite category, 96 Barsalou, Lawrence, 137–138 baseball-based caricature analogies, 325–326, 383 base-level categories, 190 basketballs as members of the category floating objects, 58 Bassok, Myriam, 345 bassoonist falling off roof as source of me-too analogy, 150–151 “Bayh”/”bye” analogy, 27 “beaucoup”, as compound word in French, broken into two concepts in English, 83 bending over backwards to accommodate contrary evidence, 291–292 Bengali poetry, as perceived by non-speakers, 343 Benserade, Isaac de, 112 betting one’s life at all moments on a myriad of trivial and unconscious analogies, 156 Bezout, Étienne, 413, 415, 420 bibles, category of 220, 229 bike-rental anomaly, explained by analogy, 328–330 bilingual data bases in machine translation, 369, 372–373 biplans: involving actions, 279; linguistic, 268–270 bird: as an example of an imprecise category, 55–56, 58, 59–60; as a platform for making inferences, 102 birds in airport/accordionist in métro analogy, 378, 380 black body: defined, 455; Max Planck and, 456–457; spectrum of, 455–459 black body/ideal gas analogy: as found by Einstein, 457–459, 463; as found by Wilhelm Wien, 458 black body/swimming pool explanatory analogy, 455, 456, 458 blended scenario, see frame blends blending, see frame blends, lexical blending blinders, categorical, 58, 290–296 blindness as result of an inability to categorize, 21 blobs, colored, in conceptual spaces, 78–81 boat in amusement park as member of category trolleycar, 521 boat on tracks as category, 521–522 body-to-body analogies, 155–156 Bohr, Niels, 143; pooh-poohing Einstein’s light quanta, 462 Bolt, Usain, 75; of cognitive science, the, 222 Boltzmann, Ludwig, 457 Bombelli, Raffaello, 440, 442 bongos on savannah in museum, 364–366 books: as abstract, immaterial entities, 7; strange types of, 83 Borges, Jorge Luis, 38, 188 “bosse” (French word), 198–200 bottle, evolution of the concept in a child’s mind, 198–200 bottlecaps on ground, see Dick at Karnak bottles thrown overboard, 284 box canyon, see impasse boxes, as misleading model of categories, 13–14, 20, 52, 54–57, 60–61, 435 brainbows, 182–184 brain tumors, analogy between two, 312–313 “brand”, evolution of meanings of, 202 brand names, genericized, 217–218 Brazilian street vendors’ arithmetic, 414–415, 422 breaking, marginal examples of the category, 41–42 bridge, as surprisingly elusive category, 67 bridges everywhere lighting up when button is pushed, 67 bridges, mental, 183–184, 336; see also analogy-making Brissiaud, Rémi, 424 Brownian motion, 458 “browse”, old-fashioned definition of, 397 “brush”, used zeugmatically, 8 “Brustwarze”, unheard parts inside, 87 bubbling-up of concepts from dormancy, 67, 170–171, 489, 491, 492, 498, 511, 513–514, 525; see also remindings, memory retrieval Buffett, Warren, 320 bumblebee, see angel stung by bumblebee bureaucratic use of acronyms, 92 Buresh, Ellie, 364–366 Buridan’s ass, 454 Bush/Schwarzenegger analogical conflation, 275 but as a category, 55, 70–75; contrasted with and, 72–75; in Russian, 74 “butter for lobster tails” joke, 358 “butterfingers”, as isolated metaphorical usage, 63–64 button #1/button #2 analogy by Monica, 169–170 buzzing interplanetary bumblebee, see randomly buzzing interplanetary bumblebee —C— c, the: in string abc, 349, 355; in string xyz, 354, 356 c2, enormous size of, 471, 482 Cairo, 75, 151, 162, 192 “camel”, marked and unmarked senses of, 199–200 Camille (who undressed the banana), 39, 41, 126 candle problem, Duncker’s, 250, 256 canine concepts, 178–181 canonization of individuals, 221–222 can-opener, universal, 439 Cantor, George, 444 “car”, marked versus unmarked senses of, 197, 230, 232 Cardano, Gerolamo, 438–440, 441, 445, 449 caricature analogies: analyzed, 320–330; blurted out, 323–324, 382–383; cascade of, 323–324; clarity as goal of, 317–318, 326–330; concreteness as force in, 329; creativity of, 324–326; diverse forms of, 320; drastic simplification in, 326; essence-spotting in, 321–322, 324–330; exaggeration as inadequate for, 321; for explaining subtle ideas to others or oneself, 326–330; feeble example of, 320; humorous baseball examples of, 325–326, 383; involving French number-words “cinq” and “six”, 380; list of, 318–320; involving Jan’s liquid and frozen assets, 476, 481, 485; mini-scenarios imagined in creation of, 323–324; mocking the timidity of Einstein’s Nobel Prize citation, 462; non-uniqueness of, 323, 325; rapidity of, 321, 323–324; reasons for concocting, 31, 317–318, 322, 324–328; search processes in, 321–322, 324–325; translation of, 380; used by the authors, 13, 18, 22, 25, 65, 108, 281, 320, 321, 337, 340, 366, 370–371, 411, 454, 462, 468, 476, 485, 497, 527 Carol signing with maiden name, 148–149 cars, blue, analogy between, 283 carving up the world in “the right way”, 14, 77, 522–523 casting pearls before swine, as category, 165 categorical blinders, 290–296, 400 categories: absurdly fine-grained, 83; ad-hoc, 137–138; base-level, 190; as blinders, 290–293, 313; blurriness in, 60, 61, 214–216, 244, 523; as boxes, 13–14, 435–436, 520, 522; of children, 39–43, 45; classical approach to, 13–14, 54–57, 435; competition between, 260–278, 281; defined by fables, 29–30, 113–118; as defining identity, 190; degree of centrality of members of, 57; development over time, 34–38, 43–45, 198–204; in discourse space, 69–76; of dogs, 178–181; dominant, 191; as drawers in a dresser, 13; extended by analogy-making, 34–38, 46, 62, 115–116, 246–248; with extremely intangible flavors, 75; as filters on perception, 292, 298–299; handed out on the silver platter of one’s language and culture, 123–124, 128–131; ideal degree of refinement of, 83–84, 108; imprecision of boundaries of, 55–61; instantly forgotten, 284; jumping unbidden to mind, 513; levels of abstraction of, 188; as the motor and fuel of cognition, 506; natural grain size of, 84; nested in the manner of Russian dolls, 520; non-lexicalized, 137, 139–140, 166–167, 176–180; organization of, as critical for expertise, 187, 237–246, 393; as organs of perception, 257, 299, 314; outnumbering words by far, 85; overly subdivided, 83; people’s frequent conflation with sets of visible objects, 54–55; private repertoire of, 166–168, 283–284; as relational, 517–519; seeming to be objectively there, 110, 111, 132–133; suburbs of, 65, 202, 213; unnoticed at their birth, 167; whose members exhibit great variety, 516; see also concepts categorization: as allowing prediction, 14–15; as applying to entities versus applying to relations, 517–519; as assignment to a schema, 336; automaticity of, 513–514; as bridge-building between two items on the same level, 519–522; carried out by analogy-making, 18–19, 179, 183–184, 309, 336, 399; as compatible with many disparities, 515–517; competition during, 261; as a conscious process, 510–513; as a constant necessity, 505; as the core of cognition, 505, 530; as creative, 508–510; described by experts exactly as analogy-making is described, 436, 506; errors in, 102–103, 527; by experts versus by novices, 342–344, 346; as fallible and misleading, 527–529; growing smoothly out of a single first instance, 182–184, 336, 520, 522; as humdrum, 508–510; identity with analogy-making, 503–530; illusion of automaticity of, 450, 513–514; as a judgment call, 117–118, 126; as jumping between two levels of abstraction, 519–522; as making the novel familiar, 436, 506; as making the world predictable, 436; as the meat and potatoes of cognition, 506; nature of, 13–15; not taught in schools, 60, 65, 126, 127; as objective, 522–526; as often being erroneous, 102–103, 527; opacity of its mechanisms, 511; “pure”, 65; rapid, as crucial for survival, 79, 83, 505–506; as rapid simplification, 505–506; reflecting one’s current perspective, 526; as reliable, 527–529; as risk-free, 527; as routine, 508–510; shades of gray in, 14; as subjective, 522–526; as suspect, 527–529; as an unconscious process, 510–513; as uncreative, 509; versus analogy-making, 434–437; as a voluntary process, 513–514; as weakened by disparities, 515–517 category boundaries, treated as sharp in everyday speech, 61 category/city analogy, 61–62, 522 category extension: via analogy, 187, 254, 395–400, 402–407; applied to proper nouns, 217–223; as an art, 468; as deep human drive, 64, 216; by Einstein, 465–468, 485–486, 495–496; by Ellenbogen, Gelenk, et al, 463–465; guiding role of language in, 465; horizontal, 463–468; as a kind of refinement, 84; and marking, 254; of number, 439–443, 447–448; from the physical world to the virtual world, 394–400; repeated acts of, 150; as revealing hidden conceptual essences, 200–204, 255, 295, 397–398; unconscious, in me-too’s, 150; vertical, 463–468; of very recent concepts, 130, 402–407; from the virtual world to the physical world, 402–407 category membership: context-dependence of, 58, 185–186; hypothetical courses in, 60, 65, 70; illusion of precision of, 59–60; illusion of uniqueness of, 58, 190, 192, 465–466; as intrinsically blurry, 60; measured by strength of analogousness, 399; necessary and sufficient conditions for, 55, 436; not taught in schools, 60, 65, 126, 127; versus playing a role in an analogy, 399 category systems: building of, as education’s goal, 393; rival, 241, 243 cat’s death, as inappropriate reminding, 157 cause–effect naïve analogy for equations, 410–411; see also operation–result centrality versus marginality of members of concepts, 57–58 chair, diversity of members of the category, 4, 5, 107 chance favoring the prepared mind, 300 Char (labrador), analogies by, 180 chat room concept, contaminated by thin wall concept, 406 chess, novices’ lack of skill in, 340 Chi, Michelene, 342 Chiflet, Jean-Loup, 97 “child” concepts modifying “parent” concepts, 53–54 children: abstraction by, 41–43; categorization by, 39–43, 45; inferences by, 391; riskily exploring usage patterns of the word “much”, 70; semantic choices made by, 41–43, 270, 273 Chinese language: concepts different from English-language counterparts, 368; Katy’s dream in, 504; “Once bitten, twice shy” in, 105; zeugmas in, 12 Chinese Pythagoras, 221 Chopin, Frédéric, 312; canonized, 221 Chrysippus, 210 chunking: of concepts over one’s lifetime, 50–54; perceptual, and esthetics, 349–352 chunks: in bilingual data base, 372–373, 375; of light, see light quanta “ciao”: competing with “grazie”, 269; competing with “salve” and “buongiorno”, 45–46 cicada, naïve analogy concerning, 388 “ciel”, vast number of meanings of, as typical, 375, 376 “Cigale et la Fourmi” (La Fontaine), 388 cigarette “melting” in ashtray, 40; as the flip side of chocolates “going up in smoke”, 126 cigarette/penis analogy, 362 “circle”, literal versus metaphorical uses of, 64 circles, non-Euclidean, 498 circular structures in Copycat domain and in real life, 355 circumference/diameter ratio, 498; see also π cities, blurriness of boundaries of, 62 city, as metaphor for concept, 61–62, 522 clairvoyance in encoding, chimera of, 173–174, 353–354 Claro, Francisco and Isabel, 312–313 classical music, category in the mind of a rock-music lover, 241 classical view of concepts, 13–14, 54–57, 435; see also Rosch, Eleanor classification versus categorization, 20 cleanliness/morality analogy, 289–290 Clement, Catherine, 436 Clément, Évelyne, 295 clocks, blocks, and rocks, 481 clothing, fringe members of the category of, 528 clouds: covering up details of sabbatical year, 50; how many in the sky?

Martin, 189–191 Glucksberg, Sam, 228 God is a sniper category, 168 Gödel, Kurt, 455 Goldstone, Robert, lexical blend by, 265 golf concepts, typical, 49–50 golf obsession, 301–302 golfer, as example of concept with halo, 49–50 Goodman, Nelson, 302 good taste versus bad taste in the Copycat domain, 349–352, 355–358; see also dizziness Google Translate: performance of, 369, 374, 377; techniques employed in, 368–369, 372–374 “Google” versus “google”, 218 gotta situations, 42 grammar: as a domain for analogy-making, 69–70; mastery of, as crucial to translation, 376–377 “grand”, broken into two concepts in French, 80 Grand Canyon seen solely as color pattern, 163; see also Danny grandmother, as marginal member of category mommy, 36–37 grandparents ⇒grandchildren conceptual slippage, 276, 356 grasshopper/human analogy, 387 gravitation/acceleration analogy, 491–492, 493–494, 496, 499 gravity: bending light, 496; having only relative existence, 494; as indistinguishable from acceleration, 491–492, 493–494, 496; as needing an explanation, yet unnoticed, 18; propagation of, across space, 489–490 gravity/electrostatics analogy, 489–491 gravity/fictitious force analogy, 491–492 “Gray Rectangle on Gray Background”, 296 Greece’s hand re Falkland Islands forced by analogy, 332 Greek letters, irrelevance of, in understanding mathematical ideas, 392–394 Grieg, Edvard, face of, 182–184, 520–522 grocery stores, navigated by analogy, 23, 156 “gros”, broken into two concepts in English, 80 groups (mathematical), 446–447, 448–449; division of one by another, 448–449 “growing smaller”, 196, 249, 413 growth of a category from sequence of instances, 182–184, 336, 520, 522 guilty and innocent as categories, 512, 514, 528–529 Gutman, Kellie, 47–49; parallel poems by, 160, 380–381 Gutman, Richard, 47–49, 159–161, 166, 380–381 Gyro Gearloose, 197 —H— h, see Planck’s constant “hacker”, old-fashioned and new definitions of, 397 halo of concepts surrounding each concept, 49–50, 62, 64, 150–151, 328, 335; constantly moving outwards, 62 hamburger: different ideas of, in American and French cultures, 122; gender of, 427; replaced by soft-drink bottle in caricature analogy, 326; used in Paul Newman’s caricature analogy, 318 hammer: as category (not) involving relationships among parts, 517–518; making everything look like a nail, 301 Hampton, James, 56 hand/foot analogy, 15, 50, 323–324 “happiest thought of my life” (Einstein), 494 Haussdorff, Felix, 444 “He who will steal an egg will steal an ox”, 106–109; upbeat interpretation of, 109 heart: as category involving relationships, 517; as member of category pump, 518 heart/finger analogy, 464–465 heart/pump analogy, 515, 518–519 heat-capacity anomaly explained by Einstein’s sound-quantum hypothesis, 461 Heisenberg, Werner, 453 “here”, as mediating mundane yet subtle analogies, 23, 142 Hertz, Heinrich, 460, 461 Herz, Hartmut, 464–465 hesitations in speech as audible traces of silently seething subterranean competition, 263, 269, 281 heureux versus heureuse, 9 hierarchy of concepts, blurriness of, 52–54 high-level perception, 452 Hilbert spaces, 444 historical precedents in wartime decisions, 17, 331–337 history repeating itself, 313; see also political analogies Hitchcock, Alfred, 59 “hither and skither”, 260, 383 Hitler, Adolf: annexing Sudetenland, 332, 334; as baby, 427; caricature analogy involving, 319; contaminating the name “Adolf”, 514; as hackneyed source for political analogies, 17; pluralized, 335; of snuggling, the, 222 Hoagland, Tony, 132 Hobbes, Thomas, 38; ranting against metaphors, 21–22 Hoffmann, Banesh, 473, 474, 477, 480, 481, 482, 495, 500–501 Hofsander, Dounuel, finishing up book in French and English on the unity of analogy-making and categorization, 529–530 Hofsander, Katyanna, as Katy/Anna fusion, 23, 32, 529–530 Hofstadter, Carol: coming up with caricature analogy, 318; driving across U.S. with family, 160; gawking at random hole, 163; lemon-sized brain tumor of, 312–313; signing with maiden name, 148–149, 174–175 Hofstadter, Danny, 283: eating water, 40; playing with ants and leaves at edge of Grand Canyon, 159–167, 171–174 Hofstadter, Douglas: choosing among greetings in Italian, 45–46; coming up with caricature analogies, 317–318; conflating glass of water with dollar bill, 280; as disillusionee and disillusioner, 171; encoding a significant event in real time, 174; as error collector, 259; falling momentarily for categories = boxes, 436; as father disappointing daughter re button, 169–170; gawking at random hole, 163; given hope by an analogy, 313; lecturing on analogies in physics, 452–453; reminded of an experience forty years later, 169–170; study and office of, 47–49; taking coffee break, 185, 317; two blue cars of, 283; watching son at Grand Canyon, 30, 159–161; as youngster enchanted by number patterns, 169–170 Hofstadter, Monica, 283: enchanted by noises from Dustbuster, 169–170, 174 Hofstadter, Oliver, as neighborhood star, 218 Hofstadter, Robert: as father disappointing son re subscripts, 169–170, 174; study and office of, 47–48 holes in the way a language fills conceptual space, see lacunæ Holyoak, Keith, 330, 436 horizontal versus vertical category extensions, 463–468 Homo sapiens sapiens versus computers, 24–25 homosexual marriage, impact on concept of marriage, 53 hub concept: as broadened from wheel center to central airport, 76, 84; internal structure of, 51–54; picture of, 51 human minds versus computers, 24–25 humor, in Copycat domain, 358, 360, 366 hump, evolution of the concept in a child’s mind, 198–200 Hunting Mister Heartbreak (Raban), 284 Hurricane Helene/lady-with-suitcase analogy, 284–286 Hussein/Hitler analogy, 135 hybrid phrases, see lexical blends hyphenated, spaced, and welded compound words, 88 —I— i (square root of –1), 445; generalized, 448 “I am like you” analogy, pervasiveness of, 156 Icelandic reminding episode, 181–182 idea choice, constrained by conversation, 26 ideal gas: defined, 457; energy spectrum of, 457, 458 ideal gas/black body analogy: found by Wilhelm Wien, 458; refound by Einstein, 457–459, 463 ideal gas/Brownian motion analogy, 458 ideal gas/pool table explanatory analogy, 135, 457–458 identity: confusion of two people’s, 224–225; intrinsic and permanent, 190, 435 idiomatic phrases in American English, list of, 95 idioms: in language A with no counterpart in language B, 119–121; meaning not deducible from constituent words, 96–98 iggfruders versus snuoiqers, 11 ignoring the surface level of word problems, difficulty of, 427–428 illusion: that category labels are mechanically retrieved, 450, 513–514; that category labels are objective, 522–526; that category labels are precise, 59–61; that category labels are unique, 58, 190, 192, 465–466; that category membership is black-and-white, 14; that concepts provided by one’s native language are monolithic, 82–83; that one’s native-language categories cut nature at the joints, 14 image-based search process, 172 imaginary numbers, gradual acceptance of, 442–443 “I’m going to pay for my beer” me-too analogy, 143–144 immaterial objects, interacting with, 252–253 impasse: caused by overhasty categorization, 258; escape from, 248–252, 255–256, 292–292; pinpointing the source of, as crucial in creativity, 256 impoverishment: of overly abstracted concepts, 107–108, 166, 204; possible utility of, 250 “in”: broken into two concepts by the French language, 78, 80; used zeugmatically, 6, 7–8 incoherent analogies in Copycat and in real life, 357–358; see also dizziness index fnger/fourth finger analogy, 464 Indianapolis hospital/Verona hospital analogy, 312 indignation, as frequent cause of caricature analogies, 317, 321 individuals, categories centered on, 221–227 Indonesian language, concept of sibling in, 77 induced structure, 345 induction: as extrapolation via analogy from the past, 307–310; parameters affecting credibility of, 308 inferences: effects of typicality on, 390–391; fallacious, due to frame-blending, 361; flowing from naïve analogies, 386; mediated by categorization, 20–21, 225, 278 infinite-dimensional spaces, 444 inner world of expectations as defining certain categories, 68 insight: incoherently mixed with literal-mindedness, 358; quartet of, found successively and exploited together, 357; thanks to caricature analogies, 326–330 in-situations, subtlety of, 7–8 instant pinpointing of timeless essences, 173–174 intelligence: and analogy-making, 126; as a function of the number of concepts one has, 128; list of various definitions of, 125; nature of, 124–126; as the pinpointing of essence, 125–126, 128–131; possibly rising steadily over time, 130; tests, as the prime venue of analogy-making, 16 intelligent ignoring and forgetfulness, 426–427 intension versus extension of a category, 55, 244 intensity of emotion as a function of strength of analogical mapping onto another person, 155 interfaces, profiting from naïve analogies, 400 interjections as categories, 46 interplanetary bumblebee, see buzzing interplanetary bumblebee intuition, alleged irrationality of, 392, 501 “invite”/”accept” caricature analogy, 319, 380 IQ scores and IQ tests, see intelligence irony, as key in encoding of Danny at the Grand Canyon, 161 irresistible analogies, 104, 155, 157, 297, 305–313 irresistible force meeting immovable object category, 326 Isis, 38 isomorphic word problems perceived differently, 429–434 Italian language: compound words in, 89; greetings in, 45–46; names of pasta types in, 243–244; zeugmas in, 8, 11 italics as a convention for concepts, 34, 110 —J— Jan, allegory of, 476, 481, 485 jargon, made mostly of everyday words, 394–400 javelin caricature of coffee-stirring sticks, 317, 321–322 Jeanine/Ruth analogical conflation, 225 Jeff, pluralization of, 223 Jewish mother category, 93–94 jiggles, ripples, rumbles, tumbles, 475 Joane (who said “Come on!”)


pages: 626 words: 181,434

I Am a Strange Loop by Douglas R. Hofstadter

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Albert Einstein, Andrew Wiles, Benoit Mandelbrot, Brownian motion, double helix, Douglas Hofstadter, Georg Cantor, Gödel, Escher, Bach, Isaac Newton, James Watt: steam engine, John Conway, John von Neumann, mandelbrot fractal, pattern recognition, Paul Erdős, place-making, probability theory / Blaise Pascal / Pierre de Fermat, publish or perish, random walk, Ronald Reagan, self-driving car, Silicon Valley, telepresence, Turing machine

Think of how the water in a glass sitting on a table seems completely still to us. If our eyes could shift levels (think of the twist that zooms binoculars in or out) and allow us to peer at the water at the micro-level, we would realize that it is not peaceful at all, but a crazy tumult of bashings of water molecules. In fact, if colloidal particles are added to a glass of water, then it becomes a locus of Brownian motion, which is an incessant random jiggling of the colloidal particles, due to a myriad of imperceptible collisions with the water molecules, which are far tinier. (The colloidal particles here play the role of simmballs, and the water molecules play the role of simms.) The effect, which is visible under a microscope, was explained in great detail in 1905 by Albert Einstein using the theory of molecules, which at the time were only hypothetical entities, but Einstein’s explanation was so far-reaching (and, most crucially, consistent with experimental data) that it became one of the most important confirmations that molecules do exist.

On a skiing vacation in the Sierra Nevada, far away from home, my children and I took advantage of the “doggie cam” at the Bloomington kennel where we had boarded our golden retriever Ollie, and thanks to the World Wide Web, we were treated to a jerky sequence of stills of a couple of dozen dogs meandering haphazardly in a fenced-in play area outdoors, looking a bit like particles undergoing random Brownian motion, and although each pooch was rendered by a pretty small array of pixels, we could often recognize our Ollie by subtle features such as the angle of his tail. For some reason, the kids and I found this act of visual eavesdropping on Ollie quite hilarious, and although we could easily describe this droll scene to our human friends, and although I would bet a considerable sum that these few lines of text have vividly evoked in your mind both the canine scene at the kennel and the human scene at the ski resort, we all realized that there was not a hope in hell that we could ever explain to Ollie himself that we had been “spying” on him from thousands of miles away.

James) Bloomington, Indiana blue humpback blueprint used in self-replicating machine blurriness of everyday concepts boat with endless succession of leaks bodies vs. souls body parts initiate self-representation Bohr atom, as stepping stone en route to quantum mechanics Bohr, Niels boiling water, reliability of Bonaparte, see Napoleon bon mots: by Carol Hofstadter; by David Moser “Book of nature written in mathematics” (Galileo) Boole, George boot-removal analogy boundaries between souls, blurriness of boundaries, macroscopic, as irrelevant to particles box with flaps making loop Brabner, George brain activity: hiddenness of substrate of; modeled computationally; need for high-level view of; obviousness of high-level view of brain-in-vat scenario brain research, nature of brain-scanning gadgets brain structures brains: compared to hearts; complexity of, as relevant to consciousness; controlling bodies directly vs. indirectly; eerieness of; evolution of; as fusion of two half-brains; as inanimate; inhabited by more than one “I”; interacting via ideas; main; as multi-level systems; not responsible for color qualia; perceiving multiple environments simultaneously; receiving sensory input directly or indirectly; resembling inert sponges; unlikely substrate for interiority Braitenberg, Valentino bread becoming a gun Brown, Charlie Brownian motion Brünn, Austria (birthplace of Kurt Gödel) buck stopping at “I” Bugeaud, Yann bunnies as edible beings “burstwise advance in evolution” (Sperry) Bushmiller, Ernie butterflies: not respecting precinct boundaries; in orchard, as metaphor for human soul Buzzaround Betty C caged-bird metaphor; as analogous to Newtonian physics; hints at wrongness of; as ingrained habit; at level of countries and cultures; metaphors opposed to; normally close to correct; as reinforced by language; temptingness of Cagey’s doubly-hearable line cake whose pieces all taste bad, as inferrred by analogy candles cantata aria Cantor, Georg capital punishment Capitalized Essences; canceled careenium; growing up; self-image of; two views of; unsatisfactory to skeptics Carnap, Rudolf Carol-and-Doug: as higher-level entity; joint mind of; shared dreads and dreams of Carolness, survival of Carol-symbol in Doug’s brain: being vs. representing a person; triggerability of cars: as high-level objects; pushed around by desires Cartesian Eggo Cartesian Ego; as commonsensical view; fading of Cartesian Ergo Cartier-Bresson, Henri Caspian Gemstones, allegory of casual façade as Searlian ploy Catcher in the Rye, The (Salinger) categories and symbols; see also repertoires categorization mechanisms: converting complexity into simplicity; as determining size of self; efficiency of Caulfield, Holden causality: bottoming out in “I”; buck of, stopping at “I”; of dogmas in triggering wars; and insight; schism between two types of; stochasticity of in everyday life; tradeoffs in; upside-down; see also downward causality causal potency: of ideas in brain; of meanings of PM strings; of patterns “causal powers of the brain”, semantic cell phones as universal machines Center for Research into Consciousness and Cognetics Central Consciousness Bank central loop of cognition cerulean sardine chain of command in brain chainium (dominos), causality in Chaitin, Greg Chalmers, David; zombie twin of chameleonic nature: of integers; of universal machines Chantal Duplessix, seeing pixel-patterns as events; missing second level of Aimable’s remarks chaos, potential, in number theory Chaplin twins, (Freda and Greta) character structure of an individual Chávez, César chemistry: bypassed in explanation of heredity and reproduction; of carbon as supposed key to consciousness; reduced to physics; virtual, inside computers “chemistry” (interpersonal); enabling people to live inside each other; as function of musical taste alignment; as highly real causal agent; as “hooked atoms”; lack of, between people “chicken” (meat) vs. chickens chickens as edible creatures children: as catalysts to soul merger of parents; as having fewer hunekers than adults; self-awareness of chimpanzees chinchillas Chinese people, as spread-out entity Chinese Room chirpy notes and deep notes interchanged Chopin, Frédéric; étude Op. 25 no. 4 in A minor; étude Op. 25 no. 11 in A minor; nostalgia of; pieces by, as soul-shards of; survival of chord–angle theorem Christiansen, Winfield church bells Church’s theorem cinnamon-roll aroma in airport corridor circular reasoning, validity of, in video feedback circumventing bans by exploiting flexible substrates clarity as central goal Class A vs.


pages: 349 words: 134,041

Traders, Guns & Money: Knowns and Unknowns in the Dazzling World of Derivatives by Satyajit Das

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accounting loophole / creative accounting, Albert Einstein, Asian financial crisis, asset-backed security, Black Swan, Black-Scholes formula, Bretton Woods, BRICs, Brownian motion, business process, buy low sell high, call centre, capital asset pricing model, collateralized debt obligation, complexity theory, corporate governance, Credit Default Swap, credit default swaps / collateralized debt obligations, cuban missile crisis, currency peg, disintermediation, diversification, diversified portfolio, Eugene Fama: efficient market hypothesis, financial innovation, fixed income, Haight Ashbury, high net worth, implied volatility, index arbitrage, index card, index fund, interest rate derivative, interest rate swap, Isaac Newton, job satisfaction, locking in a profit, Long Term Capital Management, mandelbrot fractal, margin call, market bubble, Marshall McLuhan, mass affluent, merger arbitrage, Mexican peso crisis / tequila crisis, moral hazard, mutually assured destruction, new economy, New Journalism, Nick Leeson, offshore financial centre, oil shock, Parkinson's law, placebo effect, Ponzi scheme, purchasing power parity, quantitative trading / quantitative finance, random walk, regulatory arbitrage, risk-adjusted returns, risk/return, shareholder value, short selling, South Sea Bubble, statistical model, technology bubble, the medium is the message, time value of money, too big to fail, transaction costs, value at risk, Vanguard fund, volatility smile, yield curve, Yogi Berra, zero-coupon bond

The daily price change is scaled to an annual volatility by multiplying the daily price changes by the square root of time; that is, 1% per day translates into an annual volatility of 15.81% (1% × √250 days in the year). In the world of precise high finance the business year is almost always assumed to be roughly 250 days (52 weeks × 5 days –, say, 10 public holidays). This is the root mean square rule, a common statistical trick, based on Geometric Brownian Motion (GBM). GBM describes how something like the stock price moves randomly over time from its current price in such a way that the daily price changes are distributed normally. The average price change is proportional to the square root of the elapsed time. GBM derives from the work of a botanist, Robert Brown. Brown wrote a paper entitled ‘A Brief Account of Microscopical Observations Made in the Months of June, July and August 1827, on the Particles Contained in the Pollen of Plants’.

However, the text is different. 6 ‘What Worries Warren’ (3 March 2003) Fortune. 13_INDEX.QXD 17/2/06 4:44 pm Page 325 Index accounting rules 139, 221, 228, 257 Accounting Standards Board 33 accrual accounting 139 active fund management 111 actuaries 107–10, 205, 289 Advance Corporation Tax 242 agency business 123–4, 129 agency theory 117 airline profits 140–1 Alaska 319 Allen, Woody 20 Allied Irish Bank 143 Allied Lyons 98 alternative investment strategies 112, 308 American Express 291 analysts, role of 62–4 anchor effect 136 Anderson, Rolf 92–4 annuities 204–5 ANZ Bank 277 Aquinas, Thomas 137 arbitrage 33, 38–40, 99, 114, 137–8, 171–2, 245–8, 253–5, 290, 293–6 arbitration 307 Argentina 45 arithmophobia 177 ‘armpit theory’ 303 Armstrong World Industries 274 arrears assets 225 Ashanti Goldfields 97–8, 114 Asian financial crisis (1997) 4, 9, 44–5, 115, 144, 166, 172, 207, 235, 245, 252, 310, 319 asset consultants 115–17, 281 ‘asset growth’ strategy 255 asset swaps 230–2 assets under management (AUM) 113–4, 117 assignment of loans 267–8 AT&T 275 attribution of earnings 148 auditors 144 Australia 222–4, 254–5, 261–2 back office functions 65–6 back-to-back loans 35, 40 backwardation 96 Banca Popolare di Intra 298 Bank of America 298, 303 Bank of International Settlements 50–1, 281 Bank of Japan 220 Bankers’ Trust (BT) 59, 72, 101–2, 149, 217–18, 232, 268–71, 298, 301, 319 banking regulations 155, 159, 162, 164, 281, 286, 288 banking services 34; see also commercial banks; investment banks bankruptcy 276–7 Banque Paribas 37–8, 232 Barclays Bank 121–2, 297–8 13_INDEX.QXD 17/2/06 326 4:44 pm Page 326 Index Baring, Peter 151 Baring Brothers 51, 143, 151–2, 155 ‘Basel 2’ proposal 159 basis risk 28, 42, 274 Bear Stearns 173 bearer eurodollar collateralized securities (BECS) 231–3 ‘behavioural finance’ 136 Berkshire Hathaway 19 Bermudan options 205, 227 Bernstein, Peter 167 binomial option pricing model 196 Bismarck, Otto von 108 Black, Fischer 22, 42, 160, 185, 189–90, 193, 195, 197, 209, 215 Black–Scholes formula for option pricing 22, 185, 194–5 Black–Scholes–Merton model 160, 189–93, 196–7 ‘black swan’ hypothesis 130 Blair, Tony 223 Bogle, John 116 Bohr, Niels 122 Bond, Sir John 148 ‘bond floor’ concept 251–4 bonding 75–6, 168, 181 bonuses 146–51, 244, 262, 284–5 Brady Commission 203 brand awareness and brand equity 124, 236 Brazil 302 Bretton Woods system 33 bribery 80, 303 British Sky Broadcasting (BSB) 247–8 Brittain, Alfred 72 broad index secured trust offerings (BISTROs) 284–5 brokers 69, 309 Brown, Robert 161 bubbles 210, 310, 319 Buconero 299 Buffet, Warren 12, 19–20, 50, 110–11, 136, 173, 246, 316 business process reorganization 72 business risk 159 Business Week 130 buy-backs 249 ‘call’ options 25, 90, 99, 101, 131, 190, 196 callable bonds 227–9, 256 capital asset pricing model (CAPM) 111 capital flow 30 capital guarantees 257–8 capital structure arbitrage 296 Capote, Truman 87 carbon trading 320 ‘carry cost’ model 188 ‘carry’ trades 131–3, 171 cash accounting 139 catastrophe bonds 212, 320 caveat emptor principle 27, 272 Cayman Islands 233–4 Cazenove (company) 152 CDO2 292 Cemex 249–50 chaos theory 209, 312 Chase Manhattan Bank 143, 299 Chicago Board Options Exchange 195 Chicago Board of Trade (CBOT) 25–6, 34 chief risk officers 177 China 23–5, 276, 302–4 China Club, Hong Kong 318 Chinese walls 249, 261, 280 chrematophobia 177 Citibank and Citigroup 37–8, 43, 71, 79, 94, 134–5, 149, 174, 238–9 Citron, Robert 124–5, 212–17 client relationships 58–9 Clinton, Bill 223 Coats, Craig 168–9 collateral requirements 215–16 collateralized bond obligations (CBOs) 282 collateralized debt obligations (CDOs) 45, 282–99 13_INDEX.QXD 17/2/06 4:44 pm Page 327 Index collateralized fund obligations (CFOs) 292 collateralized loan obligations (CLOs) 283–5, 288 commercial banks 265–7 commoditization 236 commodity collateralized obligations (CCOs) 292 commodity prices 304 Commonwealth Bank of Australia 255 compliance officers 65 computer systems 54, 155, 197–8 concentration risk 271, 287 conferences with clients 59 confidence levels 164 confidentiality 226 Conseco 279–80 contagion crises 291 contango 96 contingent conversion convertibles (co-cos) 257 contingent payment convertibles (co-pays) 257 Continental Illinois 34 ‘convergence’ trading 170 convertible bonds 250–60 correlations 163–6, 294–5; see also default correlations corruption 303 CORVUS 297 Cox, John 196–7 credit cycle 291 credit default swaps (CDSs) 271–84, 293, 299 credit derivatives 129, 150, 265–72, 282, 295, 299–300 Credit Derivatives Market Practices Committee 273, 275, 280–1 credit models 294, 296 credit ratings 256–7, 270, 287–8, 297–8, 304 credit reserves 140 credit risk 158, 265–74, 281–95, 299 327 credit spreads 114, 172–5, 296 Credit Suisse 70, 106, 167 credit trading 293–5 CRH Capital 309 critical events 164–6 Croesus 137 cross-ruffing 142 cubic splines 189 currency options 98, 218, 319 custom repackaged asset vehicles (CRAVEs) 233 daily earning at risk (DEAR) concept 160 Daiwa Bank 142 Daiwa Europe 277 Danish Oil and Natural Gas 296 data scrubbing 142 dealers, work of 87–8, 124–8, 133, 167, 206, 229–37, 262, 295–6; see also traders ‘death swap’ strategy 110 decentralization 72 decision-making, scientific 182 default correlations 270–1 defaults 277–9, 287, 291, 293, 296, 299 DEFCON scale 156–7 ‘Delta 1’ options 243 delta hedging 42, 200 Deming, W.E. 98, 101 Denmark 38 deregulation, financial 34 derivatives trading 5–6, 12–14, 18–72, 79, 88–9, 99–115, 123–31, 139–41, 150, 153, 155, 175, 184–9, 206–8, 211–14, 217–19, 230, 233, 257, 262–3, 307, 316, 319–20; see also equity derivatives Derman, Emmanuel 185, 198–9 Deutsche Bank 70, 104, 150, 247–8, 274, 277 devaluations 80–1, 89, 203–4, 319 13_INDEX.QXD 17/2/06 4:44 pm Page 328 328 Index dilution of share capital 241 DINKs 313 Disney Corporation 91–8 diversification 72, 110–11, 166, 299 dividend yield 243 ‘Dr Evil’ trade 135 dollar premium 35 downsizing 73 Drexel Burnham Lambert (DBL) 282 dual currency bonds 220–3; see also reverse dual currency bonds earthquakes, bonds linked to 212 efficient markets hypothesis 22, 31, 111, 203 electronic trading 126–30, 134 ‘embeddos’ 218 emerging markets 3–4, 44, 115, 132–3, 142, 212, 226, 297 Enron 54, 142, 250, 298 enterprise risk management (ERM) 176 equity capital management 249 equity collateralized obligations (ECOs) 292 equity derivatives 241–2, 246–9, 257–62 equity index 137–8 equity investment, retail market in 258–9 equity investors’ risk 286–8 equity options 253–4 equity swaps 247–8 euro currency 171, 206, 237 European Bank for Reconstruction and Development 297 European currency units 93 European Union 247–8 Exchange Rate Mechanism, European 204 exchangeable bonds 260 expatriate postings 81–2 expert witnesses 310–12 extrapolation 189, 205 extreme value theory 166 fads of management science 72–4 ‘fairway bonds’ 225 Fama, Eugene 22, 111, 194 ‘fat tail’ events 163–4 Federal Accounting Standards Board 266 Federal Home Loans Bank 213 Federal National Mortgage Association 213 Federal Reserve Bank 20, 173 Federal Reserve Board 132 ‘Ferraris’ 232 financial engineering 228, 230, 233, 249–50, 262, 269 Financial Services Authority (FSA), Japan 106, 238 Financial Services Authority (FSA), UK 15, 135 firewalls 235–6 firing of staff 84–5 First Interstate Ltd 34–5 ‘flat’ organizations 72 ‘flat’ positions 159 floaters 231–2; see also inverse floaters ‘flow’ trading 60–1, 129 Ford Motors 282, 296 forecasting 135–6, 190 forward contracts 24–33, 90, 97, 124, 131, 188 fugu fish 239 fund management 109–17, 286, 300 futures see forward contracts Galbraith, John Kenneth 121 gamma risk 200–2, 294 Gauss, Carl Friedrich 160–2 General Motors 279, 296 General Reinsurance 20 geometric Brownian motion (GBM) 161 Ghana 98 Gibson Greeting Cards 44 Glass-Steagall Act 34 gold borrowings 132 13_INDEX.QXD 17/2/06 4:44 pm Page 329 Index gold sales 97, 137 Goldman Sachs 34, 71, 93, 150, 173, 185 ‘golfing holiday bonds’ 224 Greenspan, Alan 6, 9, 19–21, 29, 43, 47, 50, 53, 62, 132, 159, 170, 215, 223, 308 Greenwich NatWest 298 Gross, Bill 19 Guangdong International Trust and Investment Corporation (GITIC) 276–7 guaranteed annuity option (GAO) contracts 204–5 Gutenfreund, John 168–9 gyosei shido 106 Haghani, Victor 168 Hamanaka, Yasuo 142 Hamburgische Landesbank 297 Hammersmith and Fulham, London Borough of 66–7 ‘hara-kiri’ swaps 39 Hartley, L.P. 163 Hawkins, Greg 168 ‘heaven and hell’ bonds 218 hedge funds 44, 88–9, 113–14, 167, 170–5, 200–2, 206, 253–4, 262–3, 282, 292, 296, 300, 308–9 hedge ratio 264 hedging 24–8, 31, 38–42, 60, 87–100, 184, 195–200, 205–7, 214, 221, 229, 252, 269, 281, 293–4, 310 Heisenberg, Werner 122 ‘hell bonds’ 218 Herman, Clement (‘Crem’) 45–9, 77, 84, 309 Herodotus 137, 178 high net worth individuals (HNWIs) 237–8, 286 Hilibrand, Lawrence 168 Hill Samuel 231–2 329 The Hitchhiker’s Guide to the Galaxy 189 Homer, Sidney 184 Hong Kong 9, 303–4 ‘hot tubbing’ 311–12 HSBC Bank 148 HSH Nordbank 297–8 Hudson, Kevin 102 Hufschmid, Hans 77–8 IBM 36, 218, 260 ICI 34 Iguchi, Toshihude 142 incubators 309 independent valuation 142 indexed currency option notes (ICONs) 218 India 302 Indonesia 5, 9, 19, 26, 55, 80–2, 105, 146, 219–20, 252, 305 initial public offerings 33, 64, 261 inside information and insider trading 133, 241, 248–9 insurance companies 107–10, 117, 119, 150, 192–3, 204–5, 221, 223, 282, 286, 300; see also reinsurance companies insurance law 272 Intel 260 intellectual property in financial products 226 Intercontinental Hotels Group (IHG) 285–6 International Accounting Standards 33 International Securities Market Association 106 International Swap Dealers Association (ISDA) 273, 275, 279, 281 Internet stock and the Internet boom 64, 112, 259, 261, 310, 319 interpolation of interest rates 141–2, 189 inverse floaters 46–51, 213–16, 225, 232–3 13_INDEX.QXD 17/2/06 4:44 pm Page 330 330 Index investment banks 34–8, 62, 64, 67, 71, 127–8, 172, 198, 206, 216–17, 234, 265–7, 298, 309 investment managers 43–4 investment styles 111–14 irrational decisions 136 Italy 106–7 Ito’s Lemma 194 Japan 39, 43, 82–3, 92, 94, 98–9, 101, 106, 132, 142, 145–6, 157, 212, 217–25, 228, 269–70 Jensen, Michael 117 Jett, Joseph 143 JP Morgan (company) 72, 150, 152, 160, 162, 249–50, 268–9, 284–5, 299; see also Morgan Guaranty junk bonds 231, 279, 282, 291, 296–7 JWM Associates 175 Kahneman, Daniel 136 Kaplanis, Costas 174 Kassouf, Sheen 253 Kaufman, Henry 62 Kerkorian, Kirk 296 Keynes, J.M. 167, 175, 198 Keynesianism 5 Kidder Peabody 143 Kleinwort Benson 40 Korea 9, 226, 278 Kozeny, Viktor 121 Krasker, William 168 Kreiger, Andy 319 Kyoto Protocol 320 Lavin, Jack 102 law of large numbers 192 Leeson, Nick 51, 131, 143, 151 legal opinions 47, 219–20, 235, 273–4 Leibowitz, Martin 184 Leland, Hayne 42, 202 Lend Lease Corporation 261–2 leptokurtic conditions 163 leverage 31–2, 48–50, 54, 99, 102–3, 114, 131–2, 171–5, 213–14, 247, 270–3, 291, 295, 305, 308 Lewis, Kenneth 303 Lewis, Michael 77–8 life insurance 204–5 Lintner, John 111 liquidity options 175 liquidity risk 158, 173 litigation 297–8 Ljunggren, Bernt 38–40 London Inter-Bank Offered Rate (LIBOR) 6, 37 ‘long first coupon’ strategy 39 Long Term Capital Management (LTCM) 44, 51, 62, 77–8, 84, 114, 166–75, 187, 206, 210, 215–18, 263–4, 309–10 Long Term Credit Bank of Japan 94 LOR (company) 202 Louisiana Purchase 319 low exercise price options (LEPOs) 261 Maastricht Treaty and criteria 106–7 McLuhan, Marshall 134 McNamara, Robert 182 macro-economic indicators, derivatives linked to 319 Mahathir Mohammed 31 Malaysia 9 management consultants 72–3 Manchester United 152 mandatory convertibles 255 Marakanond, Rerngchai 302 margin calls 97–8, 175 ‘market neutral’ investment strategy 114 market risk 158, 173, 265 marketable eurodollar collateralized securities (MECS) 232 Markowitz, Harry 110 mark-to-market accounting 10, 100, 139–41, 145, 150, 174, 215–16, 228, 244, 266, 292, 295, 298 Marx, Groucho 24, 57, 67, 117, 308 13_INDEX.QXD 17/2/06 4:44 pm Page 331 Index mathematics applied to financial instruments 209–10; see also ‘quants’ matrix structures 72 Meckling, Herbert 117 Melamed, Leo 34, 211 merchant banks 38 Meriwether, John 167–9, 172–5 Merrill Lynch 124, 150, 217, 232 Merton, Robert 22, 42, 168–70, 175, 185, 189–90, 193–7, 210 Messier, Marie 247 Metallgesellschaft 95–7 Mexico 44 mezzanine finance 285–8, 291–7 MG Refining and Marketing 95–8, 114 Microsoft 53 Mill, Stuart 130 Miller, Merton 22, 101, 194 Milliken, Michael 282 Ministry of Finance, Japan 222 misogyny 75–7 mis-selling 238, 297–8 Mitchell, Edison 70 Mitchell & Butler 275–6 models financial 42–3, 141–2, 163–4, 173–5, 181–4, 189, 198–9, 205–10 of business processes 73–5 see also credit models Modest, David 168 momentum investment 111 monetization 260–1 monopolies in financial trading 124 moral hazard 151, 280, 291 Morgan Guaranty 37–8, 221, 232 Morgan Stanley 76, 150 mortgage-backed securities (MBSs) 282–3 Moscow, City of 277 moves of staff between firms 150, 244 Mozer, Paul 169 Mullins, David 168–70 multi-skilling 73 331 Mumbai 3 Murdoch, Rupert 247 Nabisco 220 Napoleon 113 NASDAQ index 64, 112 Nash, Ogden 306 National Australia Bank 144, 178 National Rifle Association 29 NatWest Bank 144–5, 198 Niederhoffer, Victor 130 ‘Nero’ 7, 31, 45–9, 60, 77, 82–3, 88–9, 110, 118–19, 125, 128, 292 NERVA 297 New Zealand 319 Newman, Frank 104 news, financial 133–4 News Corporation 247 Newton, Isaac 162, 210 Nippon Credit Bank 106, 271 Nixon, Richard 33 Nomura Securities 218 normal distribution 160–3, 193, 199 Northern Electric 248 O’Brien, John 202 Occam, William 188 off-balance sheet transactions 32–3, 99, 234, 273, 282 ‘offsites’ 74–5 oil prices 30, 33, 89–90, 95–7 ‘omitted variable’ bias 209–10 operational risk 158, 176 opinion shopping 47 options 9, 21–2, 25–6, 32, 42, 90, 98, 124, 197, 229 pricing 185, 189–98, 202 Orange County 16, 44, 50, 124–57, 212–17, 232–3 orphan subsidiaries 234 over-the-counter (OTC) market 26, 34, 53, 95, 124, 126 overvaluation 64 13_INDEX.QXD 17/2/06 4:44 pm Page 332 332 Index ‘overwhelming force’ strategy 134–5 Owen, Martin 145 ownership, ‘legal’ and ‘economic’ 247 parallel loans 35 pari-mutuel auction system 319 Parkinson’s Law 136 Parmalat 250, 298–9 Partnoy, Frank 87 pension funds 43, 108–10, 115, 204–5, 255 People’s Bank of China (PBOC) 276–7 Peters’ Principle 71 petrodollars 71 Pétrus (restaurant) 121 Philippines, the 9 phobophobia 177 Piga, Gustavo 106 PIMCO 19 Plaza Accord 38, 94, 99, 220 plutophobia 177 pollution quotas 320 ‘portable alpha’ strategy 115 portfolio insurance 112, 202–3, 294 power reverse dual currency (PRDC) bonds 226–30 PowerPoint 75 preferred exchangeable resettable listed shares (PERLS) 255 presentations of business models 75 to clients 57, 185 prime brokerage 309 Prince, Charles 238 privatization 205 privity of contract 273 Proctor & Gamble (P&G) 44, 101–4, 155, 298, 301 product disclosure statements (PDSs) 48–9 profit smoothing 140 ‘programme’ issuers 234–5 proprietary (‘prop’) trading 60, 62, 64, 130, 174, 254 publicly available information (PAI) 277 ‘puff’ effect 148 purchasing power parity theory 92 ‘put’ options 90, 131, 256 ‘quants’ 183–9, 198, 208, 294 Raabe, Matthew 217 Ramsay, Gordon 121 range notes 225 real estate 91, 219 regulatory arbitrage 33 reinsurance companies 288–9 ‘relative value’ trading 131, 170–1, 310 Reliance Insurance 91–2 repackaging (‘repack’) business 230–6, 282, 290 replication in option pricing 195–9, 202 dynamic 200 research provided to clients 58, 62–4, 184 reserves, use of 140 reset preference shares 254–7 restructuring of loans 279–81 retail equity products 258–9 reverse convertibles 258–9 reverse dual currency bonds 223–30 ‘revolver’ loans 284–5 risk, financial, types of 158 risk adjusted return on capital (RAROC) 268, 290 risk conservation principle 229–30 risk management 65, 153–79, 184, 187, 201, 267 risk models 163–4, 173–5 riskless portfolios 196–7 RJ Reynolds (company) 220–1 rogue traders 176, 313–16 Rosenfield, Eric 168 Ross, Stephen 196–7, 202 Roth, Don 38 Rothschild, Mayer Amshel 267 Royal Bank of Scotland 298 Rubinstein, Mark 42, 196–7 13_INDEX.QXD 17/2/06 4:44 pm Page 333 Index Rumsfeld, Donald 12, 134, 306 Rusnak, John 143 Russia 45, 80, 166, 172–3, 274, 302 sales staff 55–60, 64–5, 125, 129, 217 Salomon Brothers 20, 36, 54, 62, 167–9, 174, 184 Sandor, Richard 34 Sanford, Charles 72, 269 Sanford, Eugene 269 Schieffelin, Allison 76 Scholes, Myron 22, 42, 168–71, 175, 185, 189–90, 193–7, 263–4 Seagram Group 247 Securities and Exchange Commission, US 64, 304 Securities and Futures Authority, UK 249 securitization 282–90 ‘security design’ 254–7 self-regulation 155 sex discrimination 76 share options 250–1 Sharpe, William 111 short selling 30–1, 114 Singapore 9 single-tranche CDOs 293–4, 299 ‘Sisters of Perpetual Ecstasy’ 234 SITCOMs 313 Six Continents (6C) 275–6 ‘smile’ effect 145 ‘snake’ currency system 203 ‘softing’ arrangements 117 Solon 137 Soros, George 44, 130, 253, 318–19 South Sea Bubble 210 special purpose asset repackaging companies (SPARCs) 233 special purpose vehicles (SPVs) 231–4, 282–6, 290, 293 speculation 29–31, 42, 67, 87, 108, 130 ‘spinning’ 64 333 Spitzer, Eliot 64 spread 41, 103; see also credit spreads stack hedges 96 Stamenson, Michael 124–5 standard deviation 161, 193, 195, 199 Steinberg, Sol 91 stock market booms 258, 260 stock market crashes 42–3, 168, 203, 257, 259, 319 straddles or strangles 131 strategy in banking 70 stress testing 164–6 stripping of convertible bonds 253–4 structured investment products 44, 112, 115, 118, 128, 211–39, 298 structured note asset packages (SNAPs) 233 Stuart SC 18, 307, 316–18 Styblo Bleder, Tanya 153 Suharto, Thojib 81–2 Sumitomo Corporation 100, 142 Sun Tzu 61 Svensk Exportkredit (SEK) 38–9 swaps 5–10, 26, 35–40, 107, 188, 211; see also equity swaps ‘swaptions’ 205–6 Swiss Bank Corporation (SBC) 248–9 Swiss banks 108, 305 ‘Swiss cheese theory’ 176 synthetic securitization 284–5, 288–90 systemic risk 151 Takeover Panel 248–9 Taleb, Nassim 130, 136, 167 target redemption notes 225–6 tax and tax credits 171, 242–7, 260–3 Taylor, Frederick 98, 101 team-building exercises 76 team moves 149 technical analysis 60–1, 135 television programmes about money 53, 62–3 Thailand 9, 80, 302–5 13_INDEX.QXD 17/2/06 4:44 pm Page 334 334 Index Thatcher, Margaret 205 Thorp, Edward 253 tobashi trades 105–7 Tokyo Disneyland 92, 212 top managers 72–3 total return swaps 246–8, 269 tracking error 138 traders in financial products 59–65, 129–31, 135–6, 140, 148, 151, 168, 185–6, 198; see also dealers trading limits 42, 157, 201 trading rooms 53–4, 64, 68, 75–7, 184–7, 208 Trafalgar House 248 tranching 286–9, 292, 296 transparency 26, 117, 126, 129–30, 310 Treynor, Jack 111 trust investment enhanced return securities (TIERS) 216, 233 trust obligation participating securities (TOPS) 232 TXU Europe 279 UBS Global Asset Management 110, 150, 263–4, 274 uncertainty principle 122–3 unique selling propositions 118 unit trusts 109 university education 187 unspecified fund obligations (UFOs) 292 ‘upfronting’ of income 139, 151 Valéry, Paul 163 valuation 64, 142–6 value at risk (VAR) concept 160–7, 173 value investing 111 Vanguard 116 vanity bonds 230 variance 161 Vietnam War 182, 195 Virgin Islands 233–4 Vivendi 247–8 volatility of bond prices 197 of interest rates 144–5 of share prices 161–8, 172–5, 192–3, 199 Volcker, Paul 20, 33 ‘warehouses’ 40–2, 139 warrants arbitrage 99–101 weather, bonds linked to 212, 320 Weatherstone, Dennis 72, 268 Weil, Gotscal & Manges 298 Weill, Sandy 174 Westdeutsche Genosenschafts Zentralbank 143 Westminster Group 34–5 Westpac 261–2 Wheat, Allen 70, 72, 106, 167 Wojniflower, Albert 62 World Bank 4, 36, 38 World Food Programme 320 Worldcom 250, 298 Wriston, Walter 71 WTI (West Texas Intermediate) contracts 28–30 yield curves 103, 188–9, 213, 215 yield enhancement 112, 213, 269 ‘yield hogs’ 43 zaiteku 98–101, 104–5 zero coupon bonds 221–2, 257–8


pages: 532 words: 133,143

To Explain the World: The Discovery of Modern Science by Steven Weinberg

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Albert Einstein, Alfred Russel Wallace, Astronomia nova, Brownian motion, Commentariolus, cosmological constant, dark matter, Dava Sobel, double helix, Edmond Halley, Eratosthenes, Ernest Rutherford, fudge factor, invention of movable type, Isaac Newton, James Watt: steam engine, music of the spheres, On the Revolutions of the Heavenly Spheres, probability theory / Blaise Pascal / Pierre de Fermat, retrograde motion, Thomas Kuhn: the structure of scientific revolutions

This step toward unification was resisted by some physicists, including Pierre Duhem, who doubted the existence of atoms and held that the theory of heat, thermodynamics, was at least as fundamental as Newton’s mechanics and Maxwell’s electrodynamics. But soon after the beginning of the twentieth century several new experiments convinced almost everyone that atoms are real. One series of experiments, by J. J. Thomson, Robert Millikan, and others, showed that electric charges are gained and lost only as multiples of a fundamental charge: the charge of the electron, a particle that had been discovered by Thomson in 1897. The random “Brownian” motion of small particles on the surface of liquids was interpreted by Albert Einstein in 1905 as due to collisions of these particles with individual molecules of the liquid, an interpretation confirmed by experiments of Jean Perrin. Responding to the experiments of Thomson and Perrin, the chemist Wilhelm Ostwald, who earlier had been skeptical about atoms, expressed his change of mind in 1908, in a statement that implicitly looked all the way back to Democritus and Leucippus: “I am now convinced that we have recently become possessed of experimental evidence of the discrete or grained nature of matter, which the atomic hypothesis sought in vain for hundreds and thousands of years.”4 But what are atoms?

See also equant black holes, 267 blood, circulation of, 118 Boethius of Dacia, 124–25, 128 Bohr, Niels, 261 Bokhara, sultan of, 111 Bologna, University of, 127, 147 Boltzmann, Ludwig, 259–60, 267 Bonaventure, Saint, 129 Book of the Fixed Stars (al-Sufi), 108 Born, Max, 261–62 bosons, 263, 264 Boyle, Robert, 194, 199–200, 202, 213, 217, 265 Boyle’s law, 200 Bradwardine, Thomas, 138 Brahe, Tycho. See Tycho Brahe Broglie, Louis de, 248, 261 Brownian motion, 260 Bruno, Giordano, 157, 181, 188 Bullialdus, Ismael, 226 Buridan, Jean, 71, 132–35, 137, 161, 212 Burning Sphere, The (al-Haitam), 110 Butterfield, Herbert, 145 Byzantine Empire, 103–4, 116 Caesar, Julius, 31, 50, 60 calculus, 15, 195, 223–26, 231–32, 236, 315, 327 differential, 223–25 integral, 39, 223–25 limits in, 236 calendars Antikythera Mechanism for, 71n Arabs and, 109, 116, 118 Greeks and, 56, 58–61 Gregorian, 61, 158 Julian, 61 Khayyam and, 109 Moon vs.


pages: 492 words: 149,259

Big Bang by Simon Singh

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Albert Einstein, Albert Michelson, All science is either physics or stamp collecting, Andrew Wiles, anthropic principle, Arthur Eddington, Astronomia nova, Brownian motion, carbon-based life, Cepheid variable, Chance favours the prepared mind, Commentariolus, Copley Medal, cosmic abundance, cosmic microwave background, cosmological constant, cosmological principle, dark matter, Dava Sobel, Defenestration of Prague, discovery of penicillin, Dmitri Mendeleev, Edmond Halley, Edward Charles Pickering, Eratosthenes, Ernest Rutherford, Erwin Freundlich, Fellow of the Royal Society, fudge factor, Hans Lippershey, Harlow Shapley and Heber Curtis, Harvard Computers: women astronomers, Henri Poincaré, horn antenna, if you see hoof prints, think horses—not zebras, Index librorum prohibitorum, invention of the telescope, Isaac Newton, John von Neumann, Karl Jansky, Louis Daguerre, Louis Pasteur, luminiferous ether, Magellanic Cloud, Murray Gell-Mann, music of the spheres, Olbers’ paradox, On the Revolutions of the Heavenly Spheres, Paul Erdős, retrograde motion, Richard Feynman, Richard Feynman, scientific mainstream, Simon Singh, Solar eclipse in 1919, Stephen Hawking, the scientific method, Thomas Kuhn: the structure of scientific revolutions, unbiased observer, V2 rocket, Wilhelm Olbers, William of Occam

Albert and Mileva were married in 1903, and their first son, Hans Albert, was born the next year. In 1905, while juggling the responsibilities of fatherhood and his obligations as a patent clerk, Einstein finally managed to crystallise his thoughts about the universe. His theoretical research climaxed in a burst of scientific papers which appeared in the journal Annalen der Physik. In one paper, he analysed a phenomenon known as Brownian motion and thereby presented a brilliant argument to support the theory that matter is composed of atoms and molecules. In another paper, he showed that a well-established phenomenon called the photoelectric effect could be fully explained using the newly developed theory of quantum physics. Not surprisingly, this paper went on to win Einstein a Nobel prize. The third paper, however, was even more brilliant.

Page numbers in italic refer to Figures Abell, George O. 401 absorption 235, 235, 236, 244, 245, 259 abundances, see atomic abundances Accademia del Cimento 89 Aikman, Duncan 276 Alexandria 11, 12, 13 Alfonso VI, King of Spain 33 Alfonso X, King of Castile and León 36, 76 Algol 195, 197, 198,199 al-Haytham (Alhazen) 88 alpha particles 289-92, 291, 295, 296, 297, 298,299 Alpher, Ralph 335, 471, 476, 481-3; Alpha-Beta-Gamma paper 319, 322-3,328,332,435; CMB radiation prediction 332-3,430, 434-7, 456, 473; work on nucleosynthesis 315-23,326, 390,397, 437; work on recombination 326—36, 429 Alphonsine Tables 36, 37 American Association for the Advancement of Science 227 American Astronomical Society 227 American Physical Society 460 American Telephone and Telegraph (AT&T) 402-3, 425; see also Bell Laboratories Anaxagoras 15-16, 17, 195 Anaximander 6, 7, 79 Andromeda Galaxy/Nebula 178, 179, 225; Doppler shift 247; Hubble’s distance measurement 223—6, 374—7; novae in 191-3, 222-3, 224 Annalen der Physik 107 Annates de la Société Scientifique de Bruxelles 160 anthropic principle 395, 396, 487-8 Arabs 32-3,36 Archimedes 22 Arcturus 239 Argonne National Laboratory 317 Aristarchus 15—17, 17; Sun-centred universe 22-7, 23,32, 38,41,44, 46 Aristotle 28,36,61,88 asteroids 145,479 Astrophysical Journal 432, 434, 460 Atkinson, Robert d’Escourt 300-2 atom 107,284-94,299; formation of, see nucleosynthesis; nuclear model 292—3, 294, 296, 299,368; plum pudding model 289, 289, 292, 296,368; primeval 159,269,276, 280,309; size 293-5; stability 297,299-300,310, 324-5,391; structure 292-5, 294; wavelengths 232-5, 234, 420 atomic abundances 305, 308-9, 369 388, 400,Table 4,6; hydrogen/helium 283-5,318-19,323, 327, 397 atomic bomb 311, 317 atomic number 293, 294 atomic physics 285,299 Augustine, St 492-3 Ault, Warren 217 Auteroche, Jean d’ 136 Avicenna, see Ibn Sina Baade, Walter 373-80,381, 382, 384, 414, 416 Babylonians 17-18, 28, 77 Bailey, Solon 206-7 Ball, Robert: The Story of the Heavens 194 Barberini, Francesco 74 Barnard’s Star 240 BBC 351,352 Bell, Jocelyn 167-8, 400 Bell Laboratories 402-3, 406, 422, 424—5, 431—2; horn antenna radio telescope 425-9, 427, 437, 439 Bellarmine, Cardinal 74 beryllium 391-3, 392, 396 Bessel, Friedrich Wilhelm 174-7, 176, 195 Betelgeuse 238 Bethe, Hans 303-5, 310, 319, 322 Bible 76-7, 276, 360, 362, 399 Big Bang model 3-4, 168, 254, 268-70, 336; acceptance of 438, 463; criticism of 277-83, 323, 334, 337, 341, 363-4, 378, 459, 483; forerunners of 152, 158—61; multiple 490-1; naming of 352—3, 483—4; observational evidence 252, 255,258,272, 323,430-38,460; philosophical implications 485—88; scientific method in 469-71; versus Steady State 346,347-9,359,361, 364-73,415-22, 430,432,438, 440-2, Table 4, 6; what came before it 488-92 Big Crunch 146, 480, 490-1 binary stars 145, 197-8 black holes 134, 145, 479 Bohr, Niels 491 Bond, William Cranch 204 Bondi, Hermann 340-1,345-50, 349, 384,418, 421, 438 Bonner, William 361 Born, Max 142, 338 boron 398 Brahe,Tycho 47-52, 53, 54, 71, 89, 119; De mundi ætherei 49, 50 ; model of universe 49-50, 50 Braidwood, Thomas 196 Bronstein, Matvei 363 Brownian motion 107 Bruno, Giordano 39—40; On the Infinite Universe and Worlds 39 Bunsen, Robert 237, 238 Burbidge, Geoffrey 398, 439 Burbidge, Margaret 398 Burke, Bernard 430 Buys-Ballot, Christoph 243 California Institute of Technology 272, 278, 395, 425 Cambridge 134, 412, 413, 416 Cancer,Tropic of 11, 20 Cannon, Annie Jump 206 Capra, Frank 260 carbon 304-5,308; excited state of 393-5; formation 390-5, 392, 394,396-7 Carnegie, Andrew 188,402 Carnegie Institute 187 Cassini, Giovanni Domenico 90,92 catastrophe theory 78, 147 Catholic Church 39, 41, 44, 58, 67, 70, 73-5, 484-5; banned books 70, 74; endorses Big Bang 360-2, 364; Inquisition 39, 70, 73 Cavendish Laboratory 288 centrality, illusion of 272 Cepheid variable stars 199-201, 207-10, 211, 223-6, 224; distance scale 212-13, 225, 376-7, 381; magnitude 211; populations 376-7 Chadwick, James 295-6, 302,312 Chandrasekhar, Subrahmanyan 380 chaos 326 Chicago University 186, 215, 267 Chown, Marcus 389, 457 Christian IV, King of Denmark 51 Churchill, Winston 409 circular perfection 28, 56,58 Clarke Telescope 247 Clerke, Agnes 192 Cleveland, Lemuel 227 COBE (Cosmic Background Explorer) 453-63, 458, 461, 471-3,481 Cockcroft, John 310 colour 230-5, 231 Columbia University 424 comets 147, 170, 180 computers 326 Comte, Auguste 229,237 Copernicus, Nicholas 37-47, 71,129, 367,401,485; Commentariolus 37-9; De revolutionibus 41-4, 42, 46,49,53, 63,70; errors exposed 53-4; planetary phases predicted 63-6; Sun-centred universe 38, 41, 174 cosmic density 228 cosmic microwave background (CMB) radiation 473,476,Table 4,6; detected as noise 430-8; predicted 333-4,336, 430; satellites 453-63, 458, 461,471, 481, 482; variations in 446-62, 452, 461 cosmic-ray physics 158 cosmological constant 148-9, 151-2, 153, 161, 273-4 cosmological principle 146,345; perfect 347 Coulson, Charles 484 creation 180, 261,276,284, 489-90, Table 4,6; continuous 345,347-8, 364; date of 76-7; moment of 158-9, 252-3, 255,269-70,282,344,379, 417,438 creation field (C-field) 347 creation myths 4—6 Curie, Marie and Pierre 285-7,297-8, 312 Curtis, Heber 190, 191,193-4, 224, 227 Daguerre, Louis 201 dark energy 481, 482 dark matter 280,479-80,481, 482 Darwin, Charles 3,77,350 Davis, Elmer 360 Davisson, Clinton J. 402 Dead of Night 341-4 deferents 30, 31,32, 45, 124, 367 Delta Cephei 198-9, 199 Dicke, Robert 431-2,434-5, 491 Dirac, Paul 338 Doppler, Christian 241,243,244 Doppler effect 241-8, 242,365,451; see also redshift Draper, John and Henry 204 Drydenjohn 118 dust, interstellar 193,227,407 Dyson, Frank 135 Dyson, Freeman 487 Earth 10; age of 77-8, 372, 378; composition 283; measuring 11—13, 12, 14,20,Table l; motion 24, 100-1, 405, 451, Table 2, 3; orbit around Sun 22, 119; rotation 22,38; speed through cosmos 451-2 Earth-centred universe 20—7, 23, 29, 58, 63, 72, 124, Table 2, 3; Brahe’s model 49-50, 50; Copernicus on 38-9; phases of Venus 63—5, 66; Ptolemaic model 30-6, 31,44-6, 63, 65 eclipses 197-9; lunar 10, 13, 14; solar 17, 20, 71,132-3, 135, 138-40, 141 Eddington, Arthur 134-41, 144,157, 338,476; expanding universe theory 270,280-3; and Lemaître 268-9,280; The Mathematical Theory of Relativity 135; nucleosynthesis theory 385; on rebounding universe 491; solar eclipse observations 135,137-41,143; Space, Time and Gravitation 138; on tired light theory 280 Ehrenfest, Paul 123 Egyptians 18-19,28 Einstein, Albert 24,105-7, 108, 144,191, 198; and bending of light 130-3, 140-2; and Big Bang 161,273-4,372; constancy of speed of light 103—5, 107; cosmological constant 148—9, 151-3,161,273-4; cosmology 145-9, 167,272-3; E = mc2 formula 298-9, 301; eternal, static model of universe 146-8,161, 273-4; ether thought experiment 98-103, 105, 106; and Friedmann 153-6; general relativity 116-37,143-9,153,273,345-7,471; and Lemaître 160,273-6, 275; spacetime 120—2, 121; special relativity 108-16,298-9 electromagnetic radiation 230,406, 407 electromagnetic spectrum 407, 407 electrons 292-5, 294,299, 314,328, 472 elements: formation, see nucleosynthesis; heavy 309-10,323-6,328, 385-89, 397-8,Table 5; periodic table 286-7, 287; radioactive 285—6; see also atomic abundances ellipses 54-6,55,58,119 epicycles and deferents 30, 31, 32,45, 58, 65, 66,124, 367 Eratosthenes 11-16, 12,17,19,20,177, 195 Eta Aquilae 198-9 ether 93-8, 96,101-3,141-2,145,306, 368 evolution 77,158-9, 258-60,350,360 exponential notation Table 1 Fabricius, David 58 Ferdinand, Archduke of Graz 51 Fermi, Enrico 327,380 Fernie, Donald 378 Fleming, Alexander 409 Fleming, Williamina 204, 205,206,374 Fowler, Willy 395-6,398,425 Franz Ferdinand, Archduke 133 Fraunhofer, Joseph von 237 Frederick II, King of Denmark 47, 50 Frederick Wilhelm III, King of Prussia 174 Frederiks, Vsevolod 363 Freundlich, Erwin 130,132-3 Friedmann, Alexander 150, 167, 306; expanding universe model 149—56, 249, 268; forerunner of Big Bang 254, 258,269,273,363,471,491 Fry, Art 408 galaxies 230, Table 4, 6; age of 378; distances 226, 228,372-3,376-79, 381—3; dwarf 226; expansion 271; formation 369,442-7, 451, 452, 457-62,473,477-8, 480; gravity 279; Hubble’s law 256; as nebulae 180—1, 184, 193, 219, 226; radio galaxies 405, 408, 414-20,425; recessional velocity 247-50,252-60, 253, 259,268,270-3,277, 365,373,377; redshifts 248, 252, 259,260,270,273, 277-80,282; single galaxy theory 190, 191—2,219; in Steady State universe 345, 346,348; young 348,369, 415-17 Galileo Galilei 60-75, 71,129,250,367, 401; astronomical observations 62—6, 62, 64,65-7, 66; Church and 72-4, 361,485; Dialogue Concerning the Two Chief World Systems 72-4,99; relativity principle 99-101,105,110,145; speed of light measurement 88—9; telescope 59,61-2,171,203 Gamow, George 308, 310,312, 335, 336, 364,385,471,473, 476; Alpha-Beta-Gamma paper 319,322-3,328, 332, 435; correspondence with Pope 360-1; Creation of the Universe 361, 489; critics of 323-4,332; humour 319, 325,334-5,349, 398, 399,417, 419, 420; popular science 334,351, 359,361; work on CMB radiation 333-4, 430-1, 435-7, 473; work on nucleosynthesis 306-22,326, 327, 390,397 Gauss, Carl Friedrich 472 Geiger, Hans 290-2, 291, 296 geocentric universe, see Earth-centred universe geology 78,277 George I, King of England 169 George III, King of England 169, 172, 402 George Washington University 308,311, 315,320 Gerard of Cremona 33, 36 Giese, Canon 41 Global Positioning System (GPS) 113 God 76, 79,147,180,360-1,462-3, 484-5, 488,490 gods 7,16,18 Gold, Thomas 349, 349,361, 384; on radio galaxies 413-15,418; and Steady State model 340-7, 421,438 Goodricke, John 196-8,200 gravity 25, 58, 67, 87, 200,488,Table 3; anti-gravity 148, 274; extreme 124—6, 130,144; galactic 279, 443,479; and general relativity 117,119-33,137, 144-6; Greek model 10-11, 24-5; Newtonian 118-19,122-8,137,144 Great Debate 189-94,198,201,206, 213,219-20,223-5 Greeks, Ancient 6-17,19, 33-6,79, 195; on composition of stars 238; measurements 9-17,20; nebulae 178; on planetary orbits 28—32; theory of light and sound 87—8; world-view 22—7 Grossman, Marcel 123 Grote, Harriet 214-15 Guericke, Otto von 93 Guth, Alan 477, 479, 492 H II regions 383 Haldane, J.

Quantitative Trading: How to Build Your Own Algorithmic Trading Business by Ernie Chan

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algorithmic trading, asset allocation, automated trading system, backtesting, Black Swan, Brownian motion, business continuity plan, compound rate of return, Elliott wave, endowment effect, fixed income, general-purpose programming language, index fund, Long Term Capital Management, loss aversion, p-value, paper trading, price discovery process, quantitative hedge fund, quantitative trading / quantitative finance, random walk, Ray Kurzweil, Renaissance Technologies, risk-adjusted returns, Sharpe ratio, short selling, statistical arbitrage, statistical model, systematic trading, transaction costs

Handbook of Asset and Liability Management, Volume I, Zenios and Ziemba (eds.). Elsevier 2006. Available at: www.EdwardOThorp.com. Toepke, Jerry. 2004. “Fill ‘Er Up! Benefit from Seasonal Price Patterns in Energy Futures.” Stocks, Futures and Options Magazine. March 3(3). Available at: www.sfomag.com/issuedetail.asp?MonthNameID=March& yearID=2004. Uhlenbeck, George, and Leonard Ornstein. 1930. “On the Theory of Brownian Motion.” Physical Review 36: 823–841. Van Norden, Simon, and Huntley Schaller. 1997. “Regime Switching in Stock Market Returns.” Applied Financial Economics 7: 177–191. P1: JYS bib JWBK321-Chan September 24, 2008 15:5 172 Printer: Yet to come P1: JYS ata JWBK321-Chan August 27, 2008 10:58 Printer: Yet to come About the Author rnest P. Chan is the founder of E. P. Chan & Associates (www.epchan.com), a consulting firm focusing on trading strategy and software development for money managers.


pages: 108 words: 63,808

The State of the Art by Iain M. Banks

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Brownian motion, mutually assured destruction, South China Sea

It was a TV production I'd seen on the BBC while I was in London ... or maybe the ship had repeated it. I couldn't recall. What I did recall was the plot and the setting, both of which seemed so apposite to my little scene with Linter that I started to wonder whether the beast upstairs was watching all this. Probably was, come to think of it. And not much point in looking for anything; the ship could produce bugs so small the main problem with camera stability was Brownian motion. Was The Ambassadors a sign from it then? Whatever; the play was replaced by a commercial for Odor-Eaters. 'I've told you,' Linter brought me back from my musings, speaking quietly, 'I'm prepared to take my chances. Do you think I haven't thought it all through before, many times? This isn't sudden, Sma; I felt like this my first day here, but I waited for months before I said anything, so I'd be sure.


pages: 186 words: 64,267

A Brief History of Time by Stephen Hawking

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Albert Einstein, Albert Michelson, anthropic principle, Arthur Eddington, bet made by Stephen Hawking and Kip Thorne, Brownian motion, cosmic microwave background, cosmological constant, dark matter, Edmond Halley, Ernest Rutherford, Henri Poincaré, Isaac Newton, Magellanic Cloud, Murray Gell-Mann, Richard Feynman, Richard Feynman, Stephen Hawking

For centuries the argument continued without any real evidence on either side, but in 1803 the British chemist and physicist John Dalton pointed out that the fact that chemical compounds always combined in certain proportions could be explained by the grouping together of atoms to form units called molecules. However, the argument between the two schools of thought was not finally settled in favor of the atomists until the early years of this century. One of the important pieces of physical evidence was provided by Einstein. In a paper written in 1905, a few weeks before the famous paper on special relativity, Einstein pointed out that what was called Brownian motion—the irregular, random motion of small particles of dust suspended in a liquid—could be explained as the effect of atoms of the liquid colliding with the dust particles. By this time there were already suspicions that these atoms were not, after all, indivisible. Several years previously a fellow of Trinity College, Cambridge, J. J. Thomson, had demonstrated the existence of a particle of matter, called the electron, that had a mass less than one thousandth of that of the lightest atom.

What Kind of Creatures Are We? (Columbia Themes in Philosophy) by Noam Chomsky

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Affordable Care Act / Obamacare, Albert Einstein, Arthur Eddington, Brownian motion, conceptual framework, en.wikipedia.org, failed state, Henri Poincaré, Isaac Newton, Jacques de Vaucanson, means of production, phenotype, Ronald Reagan, The Wealth of Nations by Adam Smith, theory of mind, Turing test, wage slave

Henri Poincaré went so far as to say that we adopt the molecular theory of gases only because we are familiar with the game of billiards. Ludwig Boltzmann’s scientific biographer speculates that he committed suicide because of his failure to convince the scientific community to regard his theoretical account of these matters as more than a calculating system—ironically, shortly after Albert Einstein’s work on Brownian motion and broader issues had convinced physicists of the reality of the entities he postulated. Niels Bohr’s model of the atom was also regarded as lacking “physical reality” by eminent scientists. In the 1920s, America’s first Nobel Prize–winning chemist dismissed talk about the real nature of chemical bonds as metaphysical “twaddle”: they are nothing more than “a very crude method of representing certain known facts about chemical reactions, a mode of representation” only, because the concept could not be reduced to physics.


pages: 239 words: 56,531

The Secret War Between Downloading and Uploading: Tales of the Computer as Culture Machine by Peter Lunenfeld

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Albert Einstein, Andrew Keen, Apple II, Berlin Wall, British Empire, Brownian motion, Buckminster Fuller, Burning Man, butterfly effect, computer age, crowdsourcing, cuban missile crisis, Dissolution of the Soviet Union, don't be evil, Douglas Engelbart, Dynabook, East Village, Edward Lorenz: Chaos theory, Fall of the Berlin Wall, Francis Fukuyama: the end of history, Frank Gehry, Grace Hopper, gravity well, Guggenheim Bilbao, Honoré de Balzac, Howard Rheingold, invention of movable type, Isaac Newton, Jacquard loom, Jacquard loom, Jane Jacobs, Jeff Bezos, John von Neumann, Mark Zuckerberg, Marshall McLuhan, Mercator projection, Mother of all demos, mutually assured destruction, Network effects, new economy, Norbert Wiener, PageRank, pattern recognition, planetary scale, Plutocrats, plutocrats, Post-materialism, post-materialism, Potemkin village, RFID, Richard Feynman, Richard Feynman, Richard Stallman, Robert X Cringely, Schrödinger's Cat, Search for Extraterrestrial Intelligence, SETI@home, Silicon Valley, Skype, social software, spaced repetition, Steve Ballmer, Steve Jobs, Steve Wozniak, Ted Nelson, the built environment, The Death and Life of Great American Cities, the medium is the message, Thomas L Friedman, Turing machine, Turing test, urban planning, urban renewal, Vannevar Bush, walkable city, Watson beat the top human players on Jeopardy!, William Shockley: the traitorous eight

., 123–124 Berners-Lee, Tim, 144, 167–169, 175 Bespoke futures adopting future as client and, 110–113 anticipated technology and, 108–110 crafting, 113–116 design and, 102, 105–106, 110–111, 115–116, 119–120, 124–125, 137 downloading and, 97, 123, 132, 138 dynamic equilibrium and, 117–120 89/11 and, xvi, 97, 100–102, 105, 130 Enlightenment and, xvi, 129–139 information and, 98, 100–101, 124–126 lack of vision and, 106–108 markets and, 97–104, 118, 120, 127, 131–132, 137–138 MaSAI (Massively Synchronous Applications of the Imagination) and, xvi, 112, 120–123, 127, 193n32 199 modernists and, 105–108 mutants and, 105–108 networks and, 98–101, 108, 112–113, 116, 119–126, 133, 137 New Economy and, 97, 99, 104, 131, 138, 144–145, 190n3 participation and, 98–99, 120–121, 129 plutopian meliorism and, xvi, 127–129, 133, 137–138 prosumers and, 120–121 reperceiving and, 112–113 R-PR (Really Public Relations) and, 123–127 scenario planning and, 111–119, 191n19, 192n20 simulation and, 98, 121, 124, 126–127 strange attractors and, xvi, 117–120, 192n27 technology and, 98–104, 107–113, 116, 119, 125–127, 131–133, 136–139 television and, 101, 108, 124, 127–129, 133–137 unfinish and, 127–129, 136 uploading and, 97, 120–123, 128–129, 132 Best use, 10, 13–15, 138 Bezos, Jeff, 145 Bible, 28, 137 BitTorrent, 92 Black Album, The (Jay Z), 55 Blade Runner (Scott), 107 Blogger, 177 Blogosphere, xvii bespoke futures and, 101 culture machine and, 175, 177 Facebook and, 81, 145, 180n2 stickiness and, 30, 34 Twitter and, 34, 180n2 unimodernism and, 49, 68 Web n.0 and, 80, 92–93 INDEX Bohème, La (Puccini), 61 Boing Boing magazine, 68–69 Bollywood, 62 Bourgeoisie, 31 Bowie, David, 62 Braque, Georges, 93 Breuer, Marcel, 45 Brillat-Savarin, Jean Anthèlme, 3 Brin, Sergey, 144, 174–176 Broadband technology, 9, 57 Brownian motion, 49 Burroughs, Allie Mae, 40–42 Burroughs, William, 52 Bush, Vannevar, 52, 194n6 culture machine and, 144, 147–152, 157 Engelbart and, 157 Memex and, 108, 149–151 Oppenheimer and, 150 systems theory and, 151 war effort and, 150–151 Business 2.0 magazine, 145 C3I , 146–147 Cabrini Green, 85 Calypso, 25–27 Cambodia, 107 Cambridge, 17, 36 “Can-Can” (“Orpheus in the Underworld”) (Offenbach), 62 Capitalism, 4, 13 bespoke futures and, 97–100, 103–105 Sears and, 103–105 stickiness and, 13 unimodernism and, 66, 75 Web n.0 and, 90 Capitulationism, 7, 24, 30, 182n1 Carnegie, Andrew, 166 Casablanca (film), 90 Cassette tapes, 2 CATIA 3–D software, 39 Cell phones, xiii, xvii, 17, 23, 42, 53, 56, 76, 101 Chaos theory, 117–120 Chaplin, Charlie, 45 Cheney, Dick, 99 China, 104, 107 Christians, 135 Cicero, 47 Cinema, 8, 10 micro, 56–60 stickiness and, 15 unimodernism and, 47, 52, 56–60, 63, 71 Clarke, Arthur C., 174 CNN, 58 Cobain, Kurt, 62 Code breaking, 17–18 Cold war, 101 Cole, Nat King, 62 Commercial culture, 4–5, 8 bespoke futures and, 98, 102, 108, 120, 132–134 culture machine and, 153–156, 167, 170, 172, 175–177 copyright and, 54, 88–95, 123, 164, 166, 173, 177 Mickey Mouse Protection Act and, 90 open source and, 36, 61, 69, 74–75, 91–92, 116, 121–126, 144, 170– 173, 177, 189n12 propaganda and, 124 scenario planning and, 111–119 stickiness and, 23, 28–31, 37 unimodernism and, 41, 69 Web n.0 and, 82–86 Commercial syndrome, 85–86 Communism, 97–98, 103 Compact discs (CDs), 2, 48, 53 Complex City (Simon), 39 “Computable Numbers, On” (Turing), 18 Computer Data Systems, 145 Computers, xi.


pages: 295 words: 66,824

A Mathematician Plays the Stock Market by John Allen Paulos

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Benoit Mandelbrot, Black-Scholes formula, Brownian motion, business climate, butterfly effect, capital asset pricing model, correlation coefficient, correlation does not imply causation, Daniel Kahneman / Amos Tversky, diversified portfolio, Donald Trump, double entry bookkeeping, Elliott wave, endowment effect, Erdős number, Eugene Fama: efficient market hypothesis, four colour theorem, George Gilder, global village, greed is good, index fund, invisible hand, Isaac Newton, John Nash: game theory, Long Term Capital Management, loss aversion, Louis Bachelier, mandelbrot fractal, margin call, mental accounting, Nash equilibrium, Network effects, passive investing, Paul Erdős, Ponzi scheme, price anchoring, Ralph Nelson Elliott, random walk, Richard Thaler, Robert Shiller, Robert Shiller, short selling, six sigma, Stephen Hawking, transaction costs, ultimatum game, Vanguard fund, Yogi Berra

Louis Bachelier, whom I mentioned in chapter 4, also devised a formula for options more than one hundred years ago. Bachelier’s formula was developed in connection with his famous 1900 doctoral dissertation in which he was the first to conceive of the stock market as a chance process in which price movements up and down were normally distributed. His work, which utilized the mathematical theory of Brownian motion, was way ahead of its time and hence was largely ignored. His options formula was also prescient, but ultimately misleading. (One reason for its failure is that Bachelier didn’t take account of the effect of compounding on stock returns. Over time this leads to what is called a “lognormal” distribution rather than a normal one.) The Black-Scholes options formula depends on five parameters: the present price of the stock, the length of time until the option expires, the interest rate, the strike price of the option, and the volatility of the underlying stock.


pages: 232

Planet of Slums by Mike Davis

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barriers to entry, Branko Milanovic, Bretton Woods, British Empire, Brownian motion, centre right, clean water, conceptual framework, crony capitalism, declining real wages, deindustrialization, Deng Xiaoping, edge city, European colonialism, failed state, Gini coefficient, Hernando de Soto, housing crisis, illegal immigration, income inequality, informal economy, Internet Archive, jitney, Kibera, labor-force participation, land reform, land tenure, low-wage service sector, mandelbrot fractal, market bubble, megacity, microcredit, New Urbanism, Ponzi scheme, RAND corporation, rent control, structural adjustment programs, surplus humans, upwardly mobile, urban planning, urban renewal, War on Poverty, Washington Consensus, working poor

Likewise in Bangalore, the urban fringe is where entrepreneurs can most profitably mine cheap labor with minimal oversight by the state.96 Millions of temporary workers and desperate peasants also hover around the edges of such world capitals of super-exploitation as Surat and Shenzhen. These labor nomads lack secure footing in either city or countryside, and often spend their lifetimes in a kind of desperate Brownian motion 93 See Seabrook, In the Cities of the South, p. 187. 94 Mohamadou Abdoul, "The Production of the City and Urban Informalities," in Enwezor et al. Under Siege, p. 342 95 Guy Thuillier, "Gated Communities in the Metropolitan Area of Buenos Aires," Housing Studies 20:2 (March 2005), p. 255. 96 Hans Schenk, "Urban Fringes in Asia: Markets versus Plans," in I. S. A. Baud and J. Post (eds), Realigning Actors in an Urbanising World: Governance and Institutions from a Development Perspective, Aldershot 2002, pp. 121-22, 131.


pages: 667 words: 186,968

The Great Influenza by John M. Barry

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Albert Einstein, Brownian motion, centralized clearinghouse, Chance favours the prepared mind, conceptual framework, discovery of penicillin, double helix, Fellow of the Royal Society, germ theory of disease, index card, Louis Pasteur, Marshall McLuhan, Mason jar, means of production, statistical model, the medium is the message, the scientific method, traveling salesman, women in the workforce

I have never known him to engage in purposeless rivalries or competitive research. But often have I seen him sit calmly, lost in thought, while all around him others with great show of activity were flitting about like particles in Brownian motion; then, I have watched him rouse himself, smilingly saunter to his desk, assemble a few pipettes, borrow a few tubes of media, perhaps a jar of ice, and then do a simple experiment which answered the question.” But now, in the midst of a killing epidemic, everything and everyone around him—including even the pressure from Welch—shouldered thought aside, shouldered perspective and preparation aside, substituting for it what Avery so disdained: Brownian motion—the random movement of particles in a fluid. Others hated influenza for the death it caused. Avery hated it for that, too, but for a more personal assault as well, an assault upon his integrity.


pages: 998 words: 211,235

A Beautiful Mind by Sylvia Nasar

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Al Roth, Albert Einstein, Andrew Wiles, Brownian motion, cognitive dissonance, Columbine, experimental economics, fear of failure, Henri Poincaré, invisible hand, Isaac Newton, John Conway, John Nash: game theory, John von Neumann, Kenneth Rogoff, linear programming, lone genius, market design, medical residency, Nash equilibrium, Norbert Wiener, Paul Erdős, prisoner's dilemma, RAND corporation, Ronald Coase, second-price auction, Silicon Valley, Simon Singh, spectrum auction, The Wealth of Nations by Adam Smith, Thorstein Veblen, upwardly mobile

Einstein had used to complain around the Institute that “Birkhoff is one of the world’s great academic anti-Semites.” Whether or not this was true, Birkhoff’s bias had prevented him from taking advantage of the emigration of the brilliant Jewish mathematicians from Nazi Germany.27 Indeed, Harvard also had ignored Norbert Wiener, the most brilliant American-born mathematician of his generation, the father of cybernetics and inventor of the rigorous mathematics of Brownian motion. Wiener happened to be a Jew and, like Paul Samuelson, the future Nobel Laureate in economics, he sought refuge at the far end of Cambridge at MIT, then little more than an engineering school on a par with the Carnegie Institute of Technology.28 William James, the preeminent American philosopher and older brother of the novelist Henry James, once wrote of a critical mass of geniuses causing a whole civilization to “vibrate and shake.”29 But the man in the street didn’t feel the tremors emanating from Princeton until World War II was practically over and these odd men with their funny accents, peculiar dress, and passion for obscure scientific theories became national heroes.

., 261 Brandeis University, 314–22 Brauer, Fred, 146 Brenner, Joseph, 239, 258 Brezhnev, Leonid, 332 Bricker, Jacob Leon, 144, 223, 321 Alicia Larde and, 200–201 Eleanor Stier and, 177, 178, 181, 182, 206–7 Nash’s delusions about, 326 Nash’s relationship with, 180–83, 204, 206–7 bridge, 142 Brieskorn, Egbert, 318 Brod, Max, 278 Brode, Wallace, 279 Bronx High School, 142 Brouwer’s fixed point theorem, 45, 128, 362 Browder, Earl, 153 Browder, Eva, 233–34, 380 Browder, Felix, 73, 142, 154, 157, 229, 244, 246–47 Nashes’ British trip and, 233–34 Nashes’ socializing with, 380, 386 on Nash’s defection effort, 281 Nash’s McLean commitment and, 257 Browder, William, 309, 335 Brown, Douglas, 126, 310, 312 Brownian motion, 55 Buchanan, James, 364 Buchwald, Art, 271 Bulletin de la Société Mathématique de France, 298 Bunker Hill Community College, 344 Burr, Stefan, 299 Bush, Vannevar, 137 Calabi, Eugenio, 64, 68, 72, 232, 244–45 Calabi, Giuliana, 245 calculus, tensor, 380 California Institute of Technology, 375 Camus, Albert, 271 Cantorian set theory, 52 Cappell, Sylvain, 99 Carl XVI Gustav, king of Sweden, 379–80 Carleson, Lennart, 223–24, 226, 227 Carnegie Institute of Technology, 35, 39–45, 129, 362 description of, 40 Carrier Clinic, 304, 305–8, 312–13, 43, 344 Cartan, Elie-Joseph, 157 Cartwright, Mary, 57 Casals, Pablo, 193 Castle, The (Kafka), 273, 278 Cauchy problem, 297–98 Cauvin, Jean-Pierre, 284, 298, 308 Cauvin, Louisa, 308 Central Bank of Sweden Prize in Economic Science in Memory of Alfred Nobel, see Nobel Prize in economics Central Intelligence Agency (CIA), 134 Centre de la Recherches Nationale Scientifiques, 298 Chamberlain, Gary, 354 Charles, Ray, 255 Chern, Shiing-shen, 72, 236, 279 Chiang Kai-shek, 153 Chicago, University of, 45, 132, 236, 237, 244 China, 153 Choate, Hall & Steward, 153 Chung, Kai Lai, 66 Church, Alonzo, 63, 64, 93 CIA (Central Intelligence Agency), 134 City College, 142, 144, 180 John Bates Clark medal for economics, 369 Clark University, 59 C.


pages: 740 words: 161,563

The Discovery of France by Graham Robb

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Brownian motion, deindustrialization, Honoré de Balzac, Louis Pasteur, New Economic Geography, Peace of Westphalia, price stability, trade route, urban sprawl

On the high road, for the twelve miles between Le Bouchet-St-Nicolas and Pradelles, the only other travellers he saw were ‘a cavalcade of stride-legged ladies and a pair of post-runners’, but he also saw some of the million tendrils of the other network that carried most of the traffic: The little green and stony cattle-tracks wandered in and out of one another, split into three or four, died away in marshy hollows, and began again sporadically on hillsides or at the borders of a wood. There was no direct road to Cheylard, and it was no easy affair to make a passage in this uneven country and through this intermittent labyrinth of tracks. This labyrinth is the reason why the towns and villages of France were both cut off and connected. Wares and produce travelled through the system of tracks and tiny roads by something akin to Brownian motion, changing hands slowly over great distances. When the main roads were improved and railways were built, trade was drained from the capillary network, links were broken, and a large part of the population suddenly found itself more isolated than before. Many regions today are experiencing the same effect because of the TGV railway system. * IT WOULD TAKE a thousand separate maps to show the movements of the migrant population through this labyrinth of tracks, but an excellent overall view can be gained from any large–scale relief map or satellite photograph.

link Beauvais to Amiens: Goubert, 89; also Malaucène: Saurel, I, 57–60. link fragile capillaries: Braudel, III, 228–32; Peuchet, ‘Calvados’, 10. link ‘My road lay through’: Stevenson (1879), 56. link Voie Regordane: Moch, 49–50. The name may be related to the Gaulish rigo, ‘king’. link Stevenson could have bought: Moch, quoting R. Thinthoin, 49–50. link ‘The little green and stony cattle-tracks’: Stevenson (1879), 38. link Brownian motion: Planhol, 186–7. link south and east of the line: Hufton, 72; Planhol, 242 and 285–9. link ‘Crabas amont, filhas aval’: Moch, 68. link From the . . . Cantal: Weber, 279; Wirth. link army handbook: État-major de l’armée de terre, 118. link processions of young girls: Dureau de la Malle, 250; also Gildea, 10. link loues or louées: N. Parfait, in Les Français, Province, II, 104–5; Masson de Saint-Amand, 129.


pages: 684 words: 188,584

The Age of Radiance: The Epic Rise and Dramatic Fall of the Atomic Era by Craig Nelson

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Albert Einstein, Brownian motion, cognitive dissonance, Columbine, corporate governance, cuban missile crisis, dark matter, Doomsday Clock, El Camino Real, Ernest Rutherford, failed state, Henri Poincaré, hive mind, Isaac Newton, John von Neumann, Louis Pasteur, Menlo Park, Mikhail Gorbachev, music of the spheres, mutually assured destruction, nuclear winter, oil shale / tar sands, Project Plowshare, Ralph Nader, Richard Feynman, Richard Feynman, Ronald Reagan, Skype, Stuxnet, technoutopianism, too big to fail, uranium enrichment, V2 rocket, éminence grise

After they helped her, she danced for them privately at their home and introduced them to sculptor Auguste Rodin; the four became regular friends and perhaps the only two people in the world the Curies saw regularly who weren’t scientists or blood relatives. Their closest friends remained the next-door neighbors at boulevard Kellermann, Jean and Henriette Perrin; he was a physics professor at the Sorbonne who verified Einstein’s explanation of Brownian motion, correctly estimated the size of water molecules and atoms, and established cathode rays as negatively charged particles—electrons. Pierre presented his and Marie’s scientific findings to France’s Academy of Sciences on March 16, 1903, and the Swedish Academy of Sciences then awarded them and Becquerel the Nobel Prize. Behind the scenes, four members of the French Académie had recommended that Becquerel and Pierre alone share the Nobel, leaving out Marie’s work entirely.

., 233 DuBridge, Lee, 247 Dulles, John Foster, 283 Dunning, John R., 104–05, 133 DuPont, Robert, 369–70 DuPont and Company, 131, 149, 164, 282 Dyson, Freeman, 225, 231, 262, 265, 267, 305 earthquakes, in Japan, 5, 7, 342–45, 352–53 Ebermayer, Erich, 93 Edison, Thomas, 13 Edmundson, James, 245 Eifler, Carl, 185 Einstein, Albert, 5, 34, 46, 244, 341 on atomic bomb use, 220–21 on Bohr, 94 Brownian motion explanation of, 34 childhood interest in science of, 84–85 Emergency Committee of Concerned Scientists of, 190 emigration to the United States by, 68, 80, 115 Fermi on, 66 German denunciations of, 67–68, 92, 176 on Haber, 373 as hero in popular culture, 369 on Langevin, 44 letters between Roosevelt and, 116–18, 119, 153, 176, 220, 369 Los Alamos consultations by, 153 Manhattan Project and, 83, 122 on Marie Curie, 43, 48 on Meitner, 75, 89 need for atomic bomb research advocated by, 114–15 nuclear energy and, 112, 369 nuclear warfare and 299 Oppenheimer and, 261 Planck’s research and, 87–88 on scientists and war efforts, 89 Szilard and, 77, 78, 127, 163 theory of general relativity of, 67 unified field theory of, 83 US military research and, 122 Eisenhower, Dwight D., 340, 370 arms control (Open Skies) plan of, 284, 287 arms race and, 277, 282, 286, 304 Atomic Energy Commission and, 260, 267 Atoms for Peace and, 304, 305, 331, 363 ballistic missile tracking and, 330 concern about nuclear arms use and, 255, 370 defense policy of, 283 first US nuclear power plant and, 304 military-industrial complex of, 252 missile defense shield concept and, 330 nuclear merchant ship commissioned by, 304–05 Oppenheimer and, 259–60 presidency of, 246, 252, 283 Rosenbergs’ execution and, 242 Soviet threat and, 245, 255, 256, 259 test-ban agreement and, 267 use of atomic bomb in Japan and, 208, 222 Eltenton, George¸ 261 Elugelab atoll, Mike thermonuclear tests on, 250, 251, 252–53 Emergency Committee of Concerned Scientists, 190 ENIAC computer, 248, 249 Eniwetok Island, Mike thermonuclear tests on, 250, 251, 252–53 Environmental Protection Agency (EPA), 128, 308, 310, 363 Esau, Abraham, 105 Ester, Julius, 26 Falk, Jim, 369 fallout shelters, 286, 376 Fate of the Earth, The (Schell), 299, 328 Fat Man bomb, 154, 197–98, 211, 216, 217, 230, 237, 371 FBI Bohr and, 174–75 Einstein and, 122 Fermi and, 123 Manhattan Project and, 149, 155, 171 Oppenheimer and, 155, 170, 257, 258, 260, 261, 262 spying detected by, 238–39, 240, 241, 242, 363 Szilard and, 149 Feather, Norman, 146 Fermi, Enrico, 54, 55–72, 157, 369, 379 atomic bomb design and, 168, 170, 266–67 atomic bomb testing and, 201–02, 206, 207, 229, 266–67 childhood of, 56–57 death of, 265–66, 269 decision to emigrate to the United States by, 64–65, 67, 68–72 education of, 57–58 element discovered by, 84 family life of, 123 German nuclear program and, 185 Hahn’s research on nucleus and, 103–04 Hanford reactor and, 164–65 irradiation research of, 90 legacy of, 55–56, 266, 369 Los Alamos and, 158–59, 160, 225, 228, 247 Manhattan Project and, 148, 154, 155 marriage of, 66–67, 123, 159 need for atomic bomb research advocated by, 114, 119 Nobel Prize to, 69–70, 71, 83, 97, 110, 128 nuclear fission experiment at Columbia and, 104, 105, 133 nuclear reactor design by, 129–39, 149, 160, 163, 172, 185, 233 Oak Ridge reactor and, 163 on Oppenheimer, 261 personality of, 165, 193, 225–26 political campaigns and power of, 251 postwar research at Chicago by, 225 research approach of, 123–25 research secrecy and, 112–13, 254 on scientific advances, 379 subatomic particle research of, 226 Szilard and, 229 Teller and, 147, 157, 158, 227, 228, 229, 247, 253, 265, 330 thermonuclear fusion research and, 228, 235, 247, 254 US military research and, 122–23 University of Rome research on uranium of, 58–64, 91, 266 uranium fission research of, 109–13, 124–25, 129, 266 wartime status as enemy alien, 128–29 Wigner on, 109 Fermi, Giulio, 55, 69, 71–72, 128, 226 Fermi, Laura, 55, 63–64, 65, 66–67, 69, 70, 71–72, 83, 115–16, 123–24, 126, 128, 129, 159, 170, 176, 225–26, 265, 266 Fermi, Nella, 55, 65, 70, 71–72, 123, 128, 226–27, 266, 269 Fermilab, 266 Fermi paradox, 76, 337 fermium, 253, 266 Forsmark nuclear power plant, Sweden, 312 Ferraby, Tom¸ 212 Feynman, Richard (Dick), 151, 152, 164, 166, 202, 205, 247 films, radiation theme in, 274–75, 310–11, 367 First Lightning weapons test, 233–34, 235, 238, 239, 373 Fischer, Emil, 86, 88 fishermen thermonuclear testing affecting, 273, 340 tsunami affecting, 344–45 Fitch, Val, 196, 203 Flerov, Georgi, 171–72, 193–94 Flexible Response strategy, 283, 287, 372 Fokker, Adriaan, 94, 95 Fonda, Jane, 310 France, 351, 364 Franck, James, 89, 91, 93, 207, 225 Frank, Barney, 334–35 Frayn, Michael, 181 French Academy of Sciences (Académie des Sciences), 14, 27, 34, 37, 188, 325 Frisch, David, 150 Frisch, Otto Robert, 91, 121 atomic trigger device designed by, 166–67 background of, 91 Meitner’s relationship with, 97, 189, 190 move to England by, 120 move to Los Alamos by, 152–53 nuclear fission research of Meitner and, 99–102, 103, 105, 144 thermal diffusion and, 162–63 Frisén, Jonas, 378 Fromm, Friedrich, 183 Fuchs, Elizabeth, 170–71 Fuchs, Klaus background of, 170–71 Los Alamos research by, 152, 169–70, 227, 240 spying by, 170, 171, 172, 173, 194, 237, 238, 239, 240, 251, 259 Fukushima Daiichi power plant disaster, Japan, 5, 340–60 deaths from, 360 earthquake causing, 342–45 evacuations after, 346, 349–50, 356 evidence of ancient tsunami near, 342 government regulators and, 352–53, 354 health effects of, 350, 358 heat generation from fission fragments in, 343–44, 345–46, 356 information withheld in, 350–51, 354–55 location of, 341–42 plant damage after, 347–49, 351–52, 356, 359–60 political effects of, 357, 359 private industry’s relationship with government regulators in, 353 radiation released in, 336, 355, 357, 358 rehabilitation of area and resettlement after, 358–59 steam venting in, 346–47, 349 TEPCO’s responsibilities after, 351–52 tsunami damage in, 344–45, 352–53 US consultants on, 349, 351, 355, 356 workers at, 346–48, 349, 352, 353–55, 356–57 Fuller, Loie, 33–34 Gabor, Dennis, 75, 79 Gale, Robert, 319, 349 Gamow, George, 94, 99, 248, 282 Gard, Robert, 334 Gardner, Meredith, 238, 242 Garson, Greer, 51 Garwin, Richard, 225, 247–48, 251 Geiger, Hans, 74, 87, 89, 113 Geitel, Hans Friedrich, 26 genetic abnormalities, and radiation, 326 Giannini, Gabriel Maria, 59–60 Gibertson Company, 375 Giesel, Friedrich, 31, 35, 188 Girshfield, Viktor, 290 Glicksman, Maurice, 265 Gold, Harry, 170, 172–73, 240–41, 242, 251 Goldstine, Herman, 248 Goncharov, German, 255, 275 Goodyear Tire & Rubber Company, 132, 282 Gopnik, Adam, 337 Gorbachev, Mikhail Chernobyl accident and, 318, 359, 361 International Thermonuclear Experimental Reactor (ITER) and, 364 on nuclear weapons, 328 proposed nuclear arms reduction treaty and, 329–30, 332–33 Reagan’s Strategic Defense Initiative and, 331, 332 START treaty and, 333 Göring, Hermann, 183 Goudsmit, Samuel, 186–87 Gore, Albert Sr., 293, 294 Great War (World War I), 32–33, 36, 74, 89, 91, 193, 372 Greenglass, David, 171, 172, 173, 194, 237, 240–41, 251 Greenglass, Ruth, 171, 173, 241 Greenglass, Samuel, 171 Greenewalt, Crawford, 134, 138, 164 Greisen, Kenneth, 204 Groves, Leslie Allied bombing targets recommended by, 186 atomic bomb and, 197, 198, 199, 206, 207, 202, 229 Bohr surveillance ordered by, 174–75 bombing of Japan as signal to Russia and, 222 bombing of Vemork plant, Norway, and, 178 intelligence missions of, 185–86 Los Alamos and, 151, 157, 169, 225, 228 Manhattan Project management by, 147–50, 156, 165, 175, 197–98, 199 Oak Ridge National Laboratory and, 161, 162–63 Oppenheimer and, 262 postwar atomic arms research and, 229, 230 Russian scientists and, 194 silver supply and, 161 Soviet threat and, 227 Szilard and, 127, 150, 207, 208 uranium source and, 154 Grubbe, Emil, 13 Haber, Fritz, 75, 89, 92, 372–73 Hahn, David, 362–63 Hahn, Edith, 93 Hahn, Otto Allied capture and internment of, 186–87, 188–89, 190 atomic bomb research and, 113, 121, 183, 187 awards and recognition of, 190 Hitler’s Jewish laws and, 92, 93 on Meitner, 86, 96, 98, 191 Meitner’s research with, 64, 84, 85–87, 88–90, 98, 99, 100, 102, 103, 121, 189, 190 Meitner’s treatment by, 92, 93, 96–97, 102–03, 189, 190–91 Nobel Prize to, 188–89, 190 as scientist in Nazi Germany, 190–91 Hall, Joan, 242 Hall, Theodore, 171, 194, 237, 242 Hanford, Washington, reactor complex, 159, 160, 164–65, 166, 168, 175, 188, 225, 282 Harding, Warren G., 50 Harris, Michael, 253, 272 Harrison, Richard Stewart, 144 Haukelid, Knut, 178 Havenaar, Johan, 323, 324 Hawkins, David, 192 Hawks, H.


pages: 334 words: 98,950

Bad Samaritans: The Myth of Free Trade and the Secret History of Capitalism by Ha-Joon Chang

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affirmative action, Albert Einstein, Big bang: deregulation of the City of London, bilateral investment treaty, borderless world, Bretton Woods, British Empire, Brownian motion, call centre, capital controls, central bank independence, colonial rule, Corn Laws, corporate governance, David Ricardo: comparative advantage, Deng Xiaoping, Doha Development Round, en.wikipedia.org, falling living standards, Fellow of the Royal Society, financial deregulation, fixed income, Francis Fukuyama: the end of history, income inequality, income per capita, industrial robot, Isaac Newton, joint-stock company, Joseph Schumpeter, Kenneth Rogoff, labour mobility, land reform, low skilled workers, market bubble, market fundamentalism, Martin Wolf, means of production, moral hazard, offshore financial centre, oil shock, price stability, principal–agent problem, Ronald Reagan, South Sea Bubble, structural adjustment programs, The Wealth of Nations by Adam Smith, trade liberalization, transfer pricing, urban sprawl, World Values Survey

Before the Convention went into effect in July 1884, Britain, Ecuador and Tunisia signed up, bringing the number of original member countries to 14. Subsequently, Ecuador, El Salvador and Guatemala denounced the Convention, and did not re-join it until the 1990s. The information is from the WIPO (World Intellectual Property Organization) website: http://www.wipo.int/about-ip/en/iprm/pdf/ch5.pdf#paris. 22 They were on the Brownian motion, the photoelectric effect and, most importantly, special relativity. 23 It was only in 1911, six years after he finished his Ph.D., that he was made a professor of physics in the University of Zürich. 24 For further details on the history of Swiss patent system, see Schiff (1971), Industrialisation without National Patents – the Netherlands, 1869–1912 and Switzerland, 1850–1907 (Princeton University Press, Princeton). 25 Moreover, the 1817 Dutch patent law was rather deficient even by the standards of the time.


pages: 315 words: 93,628

Is God a Mathematician? by Mario Livio

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Albert Einstein, Antoine Gombaud: Chevalier de Méré, Brownian motion, cellular automata, correlation coefficient, correlation does not imply causation, cosmological constant, Dava Sobel, double helix, Edmond Halley, Eratosthenes, Georg Cantor, Gerolamo Cardano, Gödel, Escher, Bach, Henri Poincaré, Isaac Newton, John von Neumann, music of the spheres, probability theory / Blaise Pascal / Pierre de Fermat, The Design of Experiments, the scientific method, traveling salesman

The Black-Scholes model won its originators (Myron Scholes and Robert Carhart Merton; Fischer Black passed away before the prize was awarded) the Nobel Memorial Prize in economics. The key equation in the model enables the understanding of stock option pricing (options are financial instruments that allow bidders to buy or sell stocks at a future point in time, at agreed-upon prices). Here, however, comes a surprising fact. At the heart of this model lies a phenomenon that had been studied by physicists for decades—Brownian motion, the state of agitated motion exhibited by tiny particles such as pollen suspended in water or smoke particles in the air. Then, as if that were not enough, the same equation also applies to the motion of hundreds of thousands of stars in star clusters. Isn’t this, in the language of Alice in Wonderland, “curiouser and curiouser”? After all, whatever the cosmos may be doing, business and finance are definitely worlds created by the human mind.


pages: 313 words: 101,403

My Life as a Quant: Reflections on Physics and Finance by Emanuel Derman

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Berlin Wall, bioinformatics, Black-Scholes formula, Brownian motion, capital asset pricing model, Claude Shannon: information theory, Emanuel Derman, fixed income, Gödel, Escher, Bach, haute couture, hiring and firing, implied volatility, interest rate derivative, Jeff Bezos, John von Neumann, law of one price, linked data, Long Term Capital Management, moral hazard, Murray Gell-Mann, pre–internet, publish or perish, quantitative trading / quantitative finance, Richard Feynman, Sharpe ratio, statistical arbitrage, statistical model, Stephen Hawking, Steve Jobs, stochastic volatility, technology bubble, transaction costs, value at risk, volatility smile, Y2K, yield curve, zero-coupon bond

After my experiences in physics, I never again worried too much about sharing credit with collaborators. It almost never did you harm. 1RMS is a common mnemonic for both Risk Management System and Root Mean Square.Volatility-a crucial measure of risk that is defined as the square root of the mean of the squares of the stock's daily returns, or "root mean square" in common statistical parlance. Root mean square is also suggestive of Brownian motion, the process by which a randomly moving stock price diffuses from its initial value in such a way that the average price change is proportional to the square root of the elapsed time. 'A few years later a lady who cut my hair asked for my title at work. When I said I was a Vice President at Goldman Sachs, she congratulated me on having only one person above me. She didn't understand that I was one of probably 3,000 VPs.


pages: 356 words: 95,647

Sun in a Bottle: The Strange History of Fusion and the Science of Wishful Thinking by Charles Seife

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Albert Einstein, anti-communist, Brownian motion, correlation does not imply causation, Dmitri Mendeleev, Ernest Rutherford, Fellow of the Royal Society, Gary Taubes, Isaac Newton, John von Neumann, Mikhail Gorbachev, Project Plowshare, Richard Feynman, Richard Feynman, Ronald Reagan, the scientific method, Yom Kippur War

Physicists soon joined the chemists in their support of atomic theory; they began to provide evidence for the existence of tiny atomic particles. Theorists like Ludwig Boltzmann realized that you could explain the properties of gases simply by imagining matter as a collection of atoms madly bouncing around. Observers even saw the random motion of atoms indirectly: the jostling of water molecules makes a tiny pollen grain swim erratically about. (Albert Einstein helped explain this phenomenon—Brownian motion—in 1905.) Though a few stubborn holdouts absolutely refused to believe in atomic theory,14 by the beginning of the twentieth century the scientific community was convinced. Matter was made of invisible atoms of various kinds: hydrogen atoms, oxygen atoms, carbon atoms, iron atoms, gold atoms, uranium atoms, and a few dozen others. But, as scientists were soon to find out, atoms are not quite as uncuttable as the ancient Greeks thought.


pages: 354 words: 26,550

High-Frequency Trading: A Practical Guide to Algorithmic Strategies and Trading Systems by Irene Aldridge

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algorithmic trading, asset allocation, asset-backed security, automated trading system, backtesting, Black Swan, Brownian motion, business process, capital asset pricing model, centralized clearinghouse, collapse of Lehman Brothers, collateralized debt obligation, collective bargaining, diversification, equity premium, fault tolerance, financial intermediation, fixed income, high net worth, implied volatility, index arbitrage, interest rate swap, inventory management, law of one price, Long Term Capital Management, Louis Bachelier, margin call, market friction, market microstructure, martingale, New Journalism, p-value, paper trading, performance metric, profit motive, purchasing power parity, quantitative trading / quantitative finance, random walk, Renaissance Technologies, risk tolerance, risk-adjusted returns, risk/return, Sharpe ratio, short selling, Small Order Execution System, statistical arbitrage, statistical model, stochastic process, stochastic volatility, systematic trading, trade route, transaction costs, value at risk, yield curve

In mathematical terms, if a linear model can be expressed as shown in equation (8.37), reprinted here for convenience, then nonlinear models are best expressed as shown in equation (8.38) which follows: yt = α + ∞ βi xt−i + εt (8.37) i=0 yt = f (xt , xt−1 , xt−2 , · · ·) (8.38) where {yt } is the time series of random variables that are to be forecasted, {xt } is a factor significant in forecasting {yt }, and α and β are coefficients to be estimated. The one-step-ahead nonlinear forecast conditional on the information available in the previous period is usually specified using a Brownian motion formulation, as shown in equation (8.39): yt+1 = µt+1 + σt+1 ξt+1 (8.39) forecast of the mean of the where µt+1 = Et [yt+1 ] is the one-period-ahead variable being forecasted, σt+1 = vart [xt+1 ] is the one-period-ahead forecast of the volatility of the variable being forecasted, and ξt+1 is an identically and independently distributed random variable with mean 0 and variance 1. The term ξt+1 is often referred to as a standardized shock or innovation.


pages: 353 words: 88,376

The Investopedia Guide to Wall Speak: The Terms You Need to Know to Talk Like Cramer, Think Like Soros, and Buy Like Buffett by Jack (edited By) Guinan

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Albert Einstein, asset allocation, asset-backed security, Brownian motion, business process, capital asset pricing model, clean water, collateralized debt obligation, correlation coefficient, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, discounted cash flows, diversification, diversified portfolio, dividend-yielding stocks, equity premium, fixed income, implied volatility, index fund, interest rate swap, inventory management, London Interbank Offered Rate, margin call, market fundamentalism, mortgage debt, passive investing, performance metric, risk tolerance, risk-adjusted returns, risk/return, shareholder value, Sharpe ratio, short selling, statistical model, time value of money, transaction costs, yield curve, zero-coupon bond

In contrast, less liquid assets such as a small-cap stock will have wider spreads, sometimes as high as 1 to 2% of the asset’s value. Related Terms: • Ask • Market Maker • New York Stock Exchange—NYSE • Bid • Pink Sheets Black Scholes Model What Does Black Scholes Model Mean? A model of price variation over time in financial instruments such as stocks that often is used to calculate the price of a European call option. The model assumes that the price of heavily traded assets follows a geometric Brownian motion with constant drift and volatility. When applied to a stock option, the model incorporates the constant price variation of the stock, the time value of money, the option’s strike price, and the time to the option’s expiration. Also known as the Black-Scholes-Merton Model. Investopedia explains Black Scholes Model The Black Scholes Model is one of the most important concepts in modern financial theory.


pages: 347 words: 99,317

Bad Samaritans: The Guilty Secrets of Rich Nations and the Threat to Global Prosperity by Ha-Joon Chang

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affirmative action, Albert Einstein, banking crisis, Big bang: deregulation of the City of London, bilateral investment treaty, borderless world, Bretton Woods, British Empire, Brownian motion, call centre, capital controls, central bank independence, colonial rule, Corn Laws, corporate governance, David Ricardo: comparative advantage, Deng Xiaoping, Doha Development Round, en.wikipedia.org, falling living standards, Fellow of the Royal Society, financial deregulation, fixed income, Francis Fukuyama: the end of history, income inequality, income per capita, industrial robot, Isaac Newton, joint-stock company, Joseph Schumpeter, Kenneth Rogoff, labour mobility, land reform, low skilled workers, market bubble, market fundamentalism, Martin Wolf, means of production, moral hazard, offshore financial centre, oil shock, price stability, principal–agent problem, Ronald Reagan, South Sea Bubble, structural adjustment programs, The Wealth of Nations by Adam Smith, trade liberalization, transfer pricing, urban sprawl, World Values Survey

Before the Convention went into effect in July 1884, Britain, Ecuador and Tunisia signed up, bringing the number of original member countries to 14. Subsequently, Ecuador, El Salvador and Guatemala denounced the Convention, and did not re-join it until the 1990s. The information is from the WIPO (World Intellectual Property Organization) website: http://www.wipo.int/aboutip/en/iprm/pdf/ch5.pdf#paris. 22 They were on the Brownian motion, the photoelectric effect and, most importantly, special relativity. 23 It was only in 1911, six years after he finished his Ph.D., that he was made a professor of physics in the University of Zürich. 24 For further details on the history of Swiss patent system, see Schiff (1971), Industrialisation without National Patents – the Netherlands, 1869–1912 and Switzerland, 1850–1907 (Princeton University Press, Princeton). 25 Moreover, the 1817 Dutch patent law was rather deficient even by the standards of the time.


pages: 518 words: 107,836

How Not to Network a Nation: The Uneasy History of the Soviet Internet (Information Policy) by Benjamin Peters

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Albert Einstein, Andrei Shleifer, Benoit Mandelbrot, bitcoin, Brownian motion, Claude Shannon: information theory, cloud computing, cognitive dissonance, computer age, conceptual framework, crony capitalism, crowdsourcing, cuban missile crisis, Daniel Kahneman / Amos Tversky, David Graeber, Dissolution of the Soviet Union, double helix, Drosophila, Francis Fukuyama: the end of history, From Mathematics to the Technologies of Life and Death, hive mind, index card, informal economy, invisible hand, Jacquard loom, Jacquard loom, John von Neumann, Kevin Kelly, knowledge economy, knowledge worker, linear programming, mandelbrot fractal, Marshall McLuhan, means of production, Menlo Park, Mikhail Gorbachev, mutually assured destruction, Network effects, Norbert Wiener, packet switching, pattern recognition, Paul Erdős, Peter Thiel, RAND corporation, rent-seeking, road to serfdom, Ronald Coase, scientific mainstream, Steve Jobs, Stewart Brand, stochastic process, technoutopianism, The Structural Transformation of the Public Sphere, transaction costs, Turing machine

Aleksandr Bogdanov—old Bolshevik revolutionary, right-hand man to Vladimir Lenin, and philosopher—developed a wholesale theory that analogized between society and political economy, which he published in 1913 as Tektology: A Universal Organizational Science, a proto-cybernetics minus the mathematics, whose work Wiener may have seen in translation in the 1920s or 1930s.39 Stefan Odobleja was a largely ignored Romanian whose pre–World War II work prefaced cybernetic thought.40 John von Neumann, the architect of the modern computer, a founding game theorist, and a Macy Conference participant, was a Hungarian émigré. Szolem Mandelbrojt, a Jewish Polish scientist and uncle of fractal founder Benoit Mandelbrot, organized Wiener’s collaboration on harmonic analysis and Brownian motion in 1950 in Nancy, France. Roman Jakobson, the aforementioned structural linguist, a collaborator in the Macy Conferences, and a Russian émigré, held the chair in Slavic studies at Harvard founded by Norbert Wiener’s father. And finally, Wiener’s own domineering and brilliant father, Leo Wiener, was a self-made polymath, the preeminent translator of Tolstoy into English in the twentieth-century, the founder of Slavic studies in America, an émigré from a Belarusian shtetl, and like his son, a humanist committed to uncovering methods for nearly universal communication.41 Although summarizing the intellectual and international sources for the consolidation of cybernetics as a midcentury science for self-governing systems is beyond the scope of this project, the following statement is probably not too far of a stretch.


pages: 297 words: 91,141

Market Sense and Nonsense by Jack D. Schwager

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asset allocation, Bernie Madoff, Brownian motion, collateralized debt obligation, commodity trading advisor, conceptual framework, correlation coefficient, Credit Default Swap, credit default swaps / collateralized debt obligations, Daniel Kahneman / Amos Tversky, diversification, diversified portfolio, fixed income, high net worth, implied volatility, index arbitrage, index fund, London Interbank Offered Rate, Long Term Capital Management, margin call, market bubble, market fundamentalism, merger arbitrage, pattern recognition, performance metric, pets.com, Ponzi scheme, quantitative trading / quantitative finance, random walk, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, Sharpe ratio, short selling, statistical arbitrage, statistical model, transaction costs, two-sided market, value at risk, yield curve

The efficient market hypothesis is inextricably linked to an underlying assumption that market price changes follow a random walk process (that is, price changes are normally distributed7). The assumption of a normal distribution allows one to calculate the probability of different-size price moves. Mark Rubinstein, an economist, colorfully described the improbability of the October 1987 stock market crash: Adherents of geometric Brownian motion or lognormally distributed stock returns (one of the foundation blocks of modern finance) must ever after face a disturbing fact: assuming the hypothesis that stock index returns are lognormally distributed with about a 20% annualized volatility (the historical average since 1928), the probability that the stock market could fall 29% in a single day is 10−160. So improbable is such an event that it would not be anticipated to occur even if the stock market were to last for 20 billion years, the upper end of the currently estimated duration of the universe.


pages: 312 words: 86,770

Endless Forms Most Beautiful: The New Science of Evo Devo by Sean B. Carroll

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Albert Einstein, Alfred Russel Wallace, Brownian motion, dark matter, Drosophila, Johann Wolfgang von Goethe, the scientific method

There are some excellent tutorials and animations on these authors’ Web site concerning the generation of periodic and spacing patterns: www.eb.tuebingen.mpg.de/dept4/meinhardt/home.html. François Jacob’s quotation of Jean Perrin appears in his essay “Evolution and Tinkering,” Science 196 (1977): 1161–66. Jean Perrin was a Nobel laureate in Physics (1926) who was cited for his work on colloids and Brownian motion. He wrote a very popular book, Les Atomes (1913), from which the quotation is taken. 5. The Dark Matter of the Genome: Operating Instructions for the Tool Kit I first encountered “dark matter” in Brian Greene’s The Elegant Universe (New York: W. W. Norton, 1999), a very engaging book about the structure of the universe from the very smallest to the largest scale, and in Martin Rees’s excellent Just Six Numbers: The Deep Forces That Shape the Universe (New York: Basic Books, 2001).

The Art of Computer Programming by Donald Ervin Knuth

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Brownian motion, complexity theory, correlation coefficient, Eratosthenes, Georg Cantor, information retrieval, Isaac Newton, iterative process, John von Neumann, Louis Pasteur, mandelbrot fractal, Menlo Park, NP-complete, P = NP, Paul Erdős, probability theory / Blaise Pascal / Pierre de Fermat, RAND corporation, random walk, sorting algorithm, Turing machine, Y2K

Brent, Richard Peirce, 8, 28, 40, 130, 136, 139, 141, 241, 279, 280, 313, 348, 352-353, 355, 356, 382, 386, 403, 501, 529-534, 539-540, 556, 590, 600, 643, 644, 646, 657, 695, 719-721. Brezinski, Claude, 357, 721. Brillhart, John David, 29, 394, 396, 400, 660. Brockett, Roger Ware, 712. Brocot, Achille, 655. Bronte, Emily Jane, 292. Brooks, Frederick Phillips, Jr., 226. Brouwer, Luitzen Egbertus Jan, 179. Brown, David, see Spencer Brown. Brown, George William, 135. Brown, Mark Robbin, 712. Brown, Robert, see Brownian motion. Brown, William Stanley, 419, 428, 438, 454, 686. Brownian motion, 559. Bruijn, Nicolaas Govert de, 181, 212, 568, 653, 664, 686, 694. cycle, 38-40. Brute force, 642. Bshouty, Nader Hanna (^j-i. l^ jjL>), 700. Buchholz, Werner, 202, 2~26. Bunch, James Raymond, 500. Buneman, Oscar, 706. Biirgisser, Peter, 515. Burks, Arthur Walter, 202. Burrus, Charles Sidney, 701. Butler, James Preston, 77. Butler, Michael Charles Richard, 442.

The probability that X, < x is F(x), so we have the binomial distribution discussed in Section 1.2.10: Fn(x) = s/n with probability (") F{x)s(l - F(x))n~s; the mean is F(x); the standard deviation is y/F(x)(l - F(x))/n. [See Eq. 1.2.10-(i9). This suggests that a slightly better statistic would be to define max {Fn(x) - F( — oo<x<oo see exercise 22. We can calculate the mean and standard deviation of Fn(y) — Fn(x), for x < y, and obtain the covariance of Fn(x) and Fn(y). Using these facts, it can be shown that for large values of n the function Fn(x) behaves as a "Brownian motion," and techniques from this branch of probability theory may be used to study it. The situation is exploited in articles by J. L. Doob and M. D. Donsker, Annals Math. Stat. 20 A949), 393-403 and 23 A952), 277-281; their approach is generally regarded as the most enlightening way to study the KS tests.] 7. Set j = n in Eq. A3) to see that K? is never negative, and that it can get as high as ^/n- Similarly, set j = 1 to make the same observations about K~. 8.


pages: 523 words: 148,929

Physics of the Future: How Science Will Shape Human Destiny and Our Daily Lives by the Year 2100 by Michio Kaku

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agricultural Revolution, AI winter, Albert Einstein, augmented reality, Bill Joy: nanobots, bioinformatics, blue-collar work, British Empire, Brownian motion, cloud computing, Colonization of Mars, DARPA: Urban Challenge, delayed gratification, double helix, Douglas Hofstadter, en.wikipedia.org, friendly AI, Gödel, Escher, Bach, hydrogen economy, I think there is a world market for maybe five computers, industrial robot, invention of movable type, invention of the telescope, Isaac Newton, John von Neumann, life extension, Louis Pasteur, Mahatma Gandhi, Mars Rover, megacity, Murray Gell-Mann, new economy, oil shale / tar sands, optical character recognition, pattern recognition, planetary scale, postindustrial economy, Ray Kurzweil, refrigerator car, Richard Feynman, Richard Feynman, Rodney Brooks, Ronald Reagan, Search for Extraterrestrial Intelligence, Silicon Valley, Simon Singh, speech recognition, stem cell, Stephen Hawking, Steve Jobs, telepresence, The Wealth of Nations by Adam Smith, Thomas L Friedman, Thomas Malthus, trade route, Turing machine, uranium enrichment, Vernor Vinge, Wall-E, Walter Mischel, Whole Earth Review, X Prize

Effects that we can ignore, such as van der Waals forces, surface tension, the uncertainty principle, the Pauli exclusion principle, etc., become dominant in the nanoworld. To appreciate this problem, imagine that the atom is the size of a marble and that you have a swimming pool full of these atoms. If you fell into the swimming pool, it would be quite different from falling into a swimming pool of water. These “marbles” would be constantly vibrating and hitting you from all directions, because of Brownian motion. Trying to swim in this pool would be almost impossible, since it would be like trying to swim in molasses. Every time you tried to grab one of the marbles, it would either move away from you or stick to your fingers, due to a complex combination of forces. In the end, both scientists agreed to disagree. Although Smalley was unable to throw a knockout punch against the molecular replicator, several things became clear after the dust settled.


pages: 460 words: 122,556

The End of Wall Street by Roger Lowenstein

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Asian financial crisis, asset-backed security, bank run, banking crisis, Berlin Wall, Bernie Madoff, Black Swan, Brownian motion, Carmen Reinhart, collateralized debt obligation, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, diversified portfolio, eurozone crisis, Fall of the Berlin Wall, fear of failure, financial deregulation, fixed income, high net worth, Hyman Minsky, interest rate derivative, invisible hand, Kenneth Rogoff, London Interbank Offered Rate, Long Term Capital Management, margin call, market bubble, Martin Wolf, moral hazard, mortgage debt, Northern Rock, Ponzi scheme, profit motive, race to the bottom, risk tolerance, Ronald Reagan, savings glut, short selling, sovereign wealth fund, statistical model, the payments system, too big to fail, tulip mania, Y2K

Wall Street adopted quantitative strategies because they afforded more precision than old-fashioned judgment—they seemed to convert financial gambles into hard science. Investment banks stocked risk departments with PhDs. The problem was that homeowners weren’t molecules, and finance wasn’t physics. Merrill hired John Breit, a particle theorist, as a risk manager, and Breit tried to explain to his peers that the laws of Brownian motion didn’t truly describe finance—this wasn’t science, it was pseudoscience. The models said a diversified portfolio of municipal bonds would lose money once every 10,000 years, but as Breit pointed out, such a portfolio had been devastated merely 150 years ago, during the Civil War. With regard to Merrill’s portfolio of CDOs, the firm judged its potential loss to be “$71.3 million.”6 This was absurd—not because the number was high or low, but because of the arrogance and self-delusion embedded in such fine, decimal-point precision.


pages: 286 words: 94,017

Future Shock by Alvin Toffler

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Albert Einstein, Brownian motion, Buckminster Fuller, cognitive dissonance, Colonization of Mars, corporate governance, East Village, global village, Haight Ashbury, information retrieval, invention of agriculture, invention of movable type, invention of writing, Marshall McLuhan, Menlo Park, New Urbanism, post-industrial society, RAND corporation, the market place, Thomas Kuhn: the structure of scientific revolutions, urban renewal, Whole Earth Catalog

And by attracting community and parental participation—businessmen, trade unionists, scientists, and others—the movement could build broad political support for the super-industrial revolution in education. It would be a mistake to assume that the present-day educational system is unchanging. On the contrary, it is undergoing rapid change. But much of this change is no more than an attempt to refine the existent machinery, making it ever more efficient in pursuit of obsolete goals. The rest is a kind of Brownian motion, self-canceling, incoherent, directionless. What has been lacking is a consistent direction and a logical starting point. The council movement could supply both. The direction is super-industrialism. The starting point: the future. THE ORGANIZATIONAL ATTACK Such a movement will have to pursue three objectives—to transform the organizational structure of our educational system, to revolutionize its curriculum, and to encourage a more future-focused orientation.


pages: 396 words: 117,149

The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World by Pedro Domingos

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3D printing, Albert Einstein, Amazon Mechanical Turk, Arthur Eddington, Benoit Mandelbrot, bioinformatics, Black Swan, Brownian motion, cellular automata, Claude Shannon: information theory, combinatorial explosion, computer vision, constrained optimization, correlation does not imply causation, crowdsourcing, Danny Hillis, data is the new oil, double helix, Douglas Hofstadter, Erik Brynjolfsson, experimental subject, Filter Bubble, future of work, global village, Google Glasses, Gödel, Escher, Bach, information retrieval, job automation, John Snow's cholera map, John von Neumann, Joseph Schumpeter, Kevin Kelly, lone genius, mandelbrot fractal, Mark Zuckerberg, Moneyball by Michael Lewis explains big data, Narrative Science, Nate Silver, natural language processing, Netflix Prize, Network effects, NP-complete, P = NP, PageRank, pattern recognition, phenotype, planetary scale, pre–internet, random walk, Ray Kurzweil, recommendation engine, Richard Feynman, Richard Feynman, Second Machine Age, self-driving car, Silicon Valley, speech recognition, statistical model, Stephen Hawking, Steven Levy, Steven Pinker, superintelligent machines, the scientific method, The Signal and the Noise by Nate Silver, theory of mind, transaction costs, Turing machine, Turing test, Vernor Vinge, Watson beat the top human players on Jeopardy!, white flight

Humans do it all the time: an executive can move from, say, a media company to a consumer-products one without starting from scratch because many of the same management skills still apply. Wall Street hires lots of physicists because physical and financial problems, although superficially very different, often have a similar mathematical structure. Yet all the learners we’ve seen so far would fall flat if we, say, trained them to predict Brownian motion and then asked them to predict the stock market. Stock prices and the velocities of particles suspended in a fluid are just different variables, so the learner wouldn’t even know where to start. But analogizers can do this using structure mapping, an algorithm invented by Dedre Gentner, a psychologist at Northwestern University. Structure mapping takes two descriptions, finds a coherent correspondence between some of their parts and relations, and then, based on that correspondence, transfers further properties from one structure to the other.


pages: 442 words: 39,064

Why Stock Markets Crash: Critical Events in Complex Financial Systems by Didier Sornette

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Asian financial crisis, asset allocation, Berlin Wall, Bretton Woods, Brownian motion, capital asset pricing model, capital controls, continuous double auction, currency peg, Deng Xiaoping, discrete time, diversified portfolio, Elliott wave, Erdős number, experimental economics, financial innovation, floating exchange rates, frictionless, frictionless market, full employment, global village, implied volatility, index fund, invisible hand, John von Neumann, joint-stock company, law of one price, Louis Bachelier, mandelbrot fractal, margin call, market bubble, market clearing, market design, market fundamentalism, mental accounting, moral hazard, Network effects, new economy, oil shock, open economy, pattern recognition, Paul Erdős, quantitative trading / quantitative finance, random walk, risk/return, Ronald Reagan, Schrödinger's Cat, short selling, Silicon Valley, South Sea Bubble, statistical model, stochastic process, Tacoma Narrows Bridge, technological singularity, The Coming Technological Singularity, The Wealth of Nations by Adam Smith, Tobin tax, total factor productivity, transaction costs, tulip mania, VA Linux, Y2K, yield curve

In other words, we have in mind the process of the emergence of intelligent behaviors at a macroscopic scale that individuals at the microscopic scale cannot perceive. This process has been discussed in biology, for instance in animal populations such as ant colonies or in connection with the emergence of conciousness [8, 198] Let us mention another realization of this concept, which is found in the information contained in options prices on the fluctuations of their underlying assets. Despite the fact that the prices do not follow geometrical Brownian motion, whose existence is a prerequisite for most options pricing models, traders have apparently adapted to empirically incorporating subtle information in the correlation of price distributions with fat tails [337]. In this case and in contrast to the crashes, the traders 280 chapter 7 have had time to adapt. The reason is probably that traders have been exposed for decades to options trading in which the characteristic time scale for option lifetime is in the range of month to years at most.


pages: 478 words: 142,608

The God Delusion by Richard Dawkins

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Albert Einstein, anthropic principle, Any sufficiently advanced technology is indistinguishable from magic, Ayatollah Khomeini, Brownian motion, cosmological principle, David Attenborough, Desert Island Discs, double helix, en.wikipedia.org, experimental subject, Fellow of the Royal Society, gravity well, invisible hand, John von Neumann, luminiferous ether, Menlo Park, meta analysis, meta-analysis, Murray Gell-Mann, Necker cube, Peter Singer: altruism, phenotype, placebo effect, planetary scale, Ralph Waldo Emerson, Richard Feynman, Richard Feynman, Schrödinger's Cat, Search for Extraterrestrial Intelligence, stem cell, Stephen Hawking, Steven Pinker, the scientific method, theory of mind, Thorstein Veblen, trickle-down economics, unbiased observer

The very nerve impulses with which we do our thinking and our imagining depend upon activities in Micro World. But no action that our wild ancestors ever had to perform, no decision that they ever had to take, would have been assisted by an understanding of Micro World. If we were bacteria, constantly buffeted by thermal movements of molecules, it would be different. But we Middle Worlders are too cumbersomely massive to notice Brownian motion. Similarly, our lives are dominated by gravity but are almost oblivious to the delicate force of surface tension. A small insect would reverse that priority and would find surface tension anything but delicate. Steve Grand, in Creation: Life and How to Make It, is almost scathing about our preoccupation with matter itself. We have this tendency to think that only solid, material ‘things’ are ‘really’ things at all.


pages: 504 words: 139,137

Efficiently Inefficient: How Smart Money Invests and Market Prices Are Determined by Lasse Heje Pedersen

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algorithmic trading, Andrei Shleifer, asset allocation, backtesting, bank run, banking crisis, barriers to entry, Black-Scholes formula, Brownian motion, buy low sell high, capital asset pricing model, commodity trading advisor, conceptual framework, corporate governance, credit crunch, Credit Default Swap, currency peg, David Ricardo: comparative advantage, declining real wages, discounted cash flows, diversification, diversified portfolio, Emanuel Derman, equity premium, Eugene Fama: efficient market hypothesis, fixed income, Flash crash, floating exchange rates, frictionless, frictionless market, Gordon Gekko, implied volatility, index arbitrage, index fund, interest rate swap, late capitalism, law of one price, Long Term Capital Management, margin call, market clearing, market design, market friction, merger arbitrage, mortgage debt, New Journalism, paper trading, passive investing, price discovery process, price stability, purchasing power parity, quantitative easing, quantitative trading / quantitative finance, random walk, Renaissance Technologies, Richard Thaler, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, shareholder value, Sharpe ratio, short selling, sovereign wealth fund, statistical arbitrage, statistical model, systematic trading, technology bubble, time value of money, total factor productivity, transaction costs, value at risk, Vanguard fund, yield curve, zero-coupon bond

In its most extreme form, it says not only that markets discount the future, but they accurately reflect all fundamentals of economies and everything that’s known about companies and so on and so forth, and they synthesize this information into completely perfect prices. This theory would be laughable if it wasn’t so widely believed in. It’s come out of valuing options and modeling diffusion processes: price movement as a diffusion using the Brownian motion and the heat equation. That is a good approximation for modeling short-term options, but to extend that to the idea that there is this perfect matrix of prices that reflects everything perfectly is putting too much weight on a small base of evidence, as they say in science. LHP: So how do your models exploit that markets are not perfectly efficient? DWH: Markets are social institutions and reflect all sorts of phenomena that you’d expect such social institutions to reflect.


pages: 509 words: 132,327

Rise of the Machines: A Cybernetic History by Thomas Rid

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1960s counterculture, A Declaration of the Independence of Cyberspace, agricultural Revolution, Albert Einstein, Alistair Cooke, Apple II, Apple's 1984 Super Bowl advert, back-to-the-land, Berlin Wall, British Empire, Brownian motion, Buckminster Fuller, business intelligence, Claude Shannon: information theory, conceptual framework, connected car, domain-specific language, Douglas Engelbart, dumpster diving, Extropian, full employment, game design, global village, Haight Ashbury, Howard Rheingold, Jaron Lanier, job automation, John von Neumann, Kevin Kelly, Marshall McLuhan, Menlo Park, Mother of all demos, new economy, New Journalism, Norbert Wiener, offshore financial centre, oil shale / tar sands, pattern recognition, RAND corporation, Silicon Valley, Simon Singh, speech recognition, Steve Jobs, Steve Wozniak, Steven Levy, Stewart Brand, technoutopianism, Telecommunications Act of 1996, telepresence, V2 rocket, Vernor Vinge, Whole Earth Catalog, Whole Earth Review, Y2K, Yom Kippur War, Zimmermann PGP

It didn’t mention the unsuccessful experiments in the little MIT lab or any mechanical implementation of his theory. The paper mentioned the antiaircraft problem only two times, buried in a forest of mathematical formulas on page 76. Neither the title nor the introduction or index contained a single reference to the problem that had motivated the project’s funding. Instead, Wiener offered a mind-numbing alphabet soup of abstruse mathematics: Brownian motion, Cesàro partial sum, Fourier integral, Hermitian form, Lebesgue measure, Parseval’s theorem, Poisson distribution, Schwarz inequality, Stieltjes integral, Weyl’s lemma, and many more. When Weaver received the paper, he had it classified and bound in an orange cover. Engineers nicknamed the document “yellow peril,” a joking reference to the paper’s impenetrable theory and lack of practical relevance.

How I Became a Quant: Insights From 25 of Wall Street's Elite by Richard R. Lindsey, Barry Schachter

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Albert Einstein, algorithmic trading, Andrew Wiles, Antoine Gombaud: Chevalier de Méré, asset allocation, asset-backed security, backtesting, bank run, banking crisis, Black-Scholes formula, Bonfire of the Vanities, Bretton Woods, Brownian motion, business process, buy low sell high, capital asset pricing model, centre right, collateralized debt obligation, corporate governance, correlation coefficient, Credit Default Swap, credit default swaps / collateralized debt obligations, currency manipulation / currency intervention, discounted cash flows, disintermediation, diversification, Emanuel Derman, en.wikipedia.org, Eugene Fama: efficient market hypothesis, financial innovation, fixed income, full employment, George Akerlof, Gordon Gekko, hiring and firing, implied volatility, index fund, interest rate derivative, interest rate swap, John von Neumann, linear programming, Loma Prieta earthquake, Long Term Capital Management, margin call, market friction, market microstructure, martingale, merger arbitrage, Nick Leeson, P = NP, pattern recognition, pensions crisis, performance metric, prediction markets, profit maximization, purchasing power parity, quantitative trading / quantitative finance, QWERTY keyboard, RAND corporation, random walk, Ray Kurzweil, Richard Feynman, Richard Feynman, Richard Stallman, risk-adjusted returns, risk/return, shareholder value, Sharpe ratio, short selling, Silicon Valley, six sigma, sorting algorithm, statistical arbitrage, statistical model, stem cell, Steven Levy, stochastic process, systematic trading, technology bubble, The Great Moderation, the scientific method, too big to fail, trade route, transaction costs, transfer pricing, value at risk, volatility smile, Wiener process, yield curve, young professional

I, on the other hand, muddled along, testing model after model to little effect, all the while trying to make sense of my surroundings. I was to discover that graduate school had prepared me in a decidedly tangential manner for what I was to encounter. The foreign exchange markets, which I had studied extensively in the context of purchasing power parity, uncovered interest rate parity, and geometric JWPR007-Lindsey April 30, 2007 18:3 Andrew B. Weisman 189 Brownian motion, were almost unrecognizable to me. I frequently felt lost in a world of rapid-fire economic and political developments, blaring broker boxes, and arcane market nomenclature. It was as if I had embarked on a career as a professional pugilist armed with an extensive knowledge of anatomy and the basic instruction set that I must strike my opponent firmly about the head and abdomen while avoiding same.


pages: 692 words: 127,032

Fool Me Twice: Fighting the Assault on Science in America by Shawn Lawrence Otto

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affirmative action, Albert Einstein, anthropic principle, Berlin Wall, Brownian motion, carbon footprint, Cepheid variable, clean water, Climategate, Climatic Research Unit, cognitive dissonance, Columbine, cosmological constant, crowdsourcing, cuban missile crisis, Dean Kamen, desegregation, double helix, energy security, Exxon Valdez, fudge factor, ghettoisation, Harlow Shapley and Heber Curtis, Harvard Computers: women astronomers, informal economy, invisible hand, Isaac Newton, Louis Pasteur, mutually assured destruction, Richard Feynman, Richard Feynman, Ronald Reagan, Saturday Night Live, shareholder value, sharing economy, smart grid, Solar eclipse in 1919, stem cell, the scientific method, The Wealth of Nations by Adam Smith, Thomas Kuhn: the structure of scientific revolutions, transaction costs, University of East Anglia, War on Poverty, white flight, Winter of Discontent, working poor

They do not extend in sudden and dramatic paradigm shifts, and they didn’t in Einstein’s day, either. In fact, many of the ideas Einstein developed were done collaboratively, with considerable debate, a prime example being the cosmological constant. His early papers were extensions of the work of Max Planck, the Austrian physicist Ludwig Boltzmann, and others, and his revolutionary findings on Brownian motion were independently discovered by Polish physicist Marian von Smoluchowski, who was also building on Boltzmann’s work. Hubble’s revolutionary discovery of the expansion of the universe also extended from ideas that were talked about for years. The redshift was first noted by American astronomer Vesto Slipher in 1912—nearly two decades before Hubble’s discovery. Galileo’s revolution was an extension of Copernicus’s writings of some seventy years before, which were widely discussed.

The Science of Language by Noam Chomsky

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Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Alfred Russel Wallace, British Empire, Brownian motion, dark matter, Drosophila, epigenetics, finite state, Howard Zinn, phenotype, statistical model, stem cell, Steven Pinker, theory of mind

Even great scientists, such as, say, Poincaré – one of the twentieth century's greatest scientists – just laughed at it. [Those who laughed] were very much under Machian [Ernst Mach's] influence: if you can't see it, touch it . . . [you can't take it seriously]; so you just have a way of calculating. Boltzmann actually committed suicide – in part, apparently, because of his inability to get anyone to take him seriously. By a horrible irony, he did it in 1905, the year that Einstein's Brownian motion paper came out, and everyone began to take it seriously. And it goes on. I've been interested in the history of chemistry. Into the 1920s, when I was born – so it isn't that far back – leading scientists would have just ridiculed the idea of taking any of this seriously, including Nobel prizewinning chemists. They thought of [atoms and other such ‘devices’] as ways of calculating the results of experiments.


pages: 645 words: 184,311

American Gods by Neil Gaiman

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airport security, book scanning, Brownian motion, Golden Gate Park, Lao Tzu

Shadow had never seen the Nile, but there was a blinding afternoon sun burning on the wide brown river that made him think of the muddy expanse of the Nile: not the Nile as it is now, but as it was long ago, flowing like an artery through the papyrus marshes, home to cobra and jackal and wild cow... A road sign pointed to Thebes. The road was built up about twelve feet, so he was driving above the marshes. Clumps and clusters of birds in flight were questing back and forth, black dots against the blue sky, moving in some desperate Brownian motion. In the late afternoon the sun began to lower, gilding the world in elf-light, a thick warm custardy light that made the world feel unearthly and more than real, and it was in this light that Shadow passed the sign telling him he was Now Entering Historical Cairo. He drove under a bridge and found himself in a small port town. The imposing structures of the Cairo courthouse and the even more imposing customs house looked like enormous freshly baked cookies in the syrupy gold of the light at the end of the day.


pages: 678 words: 216,204

The Wealth of Networks: How Social Production Transforms Markets and Freedom by Yochai Benkler

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affirmative action, barriers to entry, bioinformatics, Brownian motion, call centre, Cass Sunstein, centre right, clean water, dark matter, desegregation, East Village, fear of failure, Firefox, game design, George Gilder, hiring and firing, Howard Rheingold, informal economy, invention of radio, Isaac Newton, iterative process, Jean Tirole, jimmy wales, market bubble, market clearing, Marshall McLuhan, New Journalism, optical character recognition, pattern recognition, pre–internet, price discrimination, profit maximization, profit motive, random walk, recommendation engine, regulatory arbitrage, rent-seeking, RFID, Richard Stallman, Ronald Coase, Search for Extraterrestrial Intelligence, SETI@home, shareholder value, Silicon Valley, Skype, slashdot, social software, software patent, spectrum auction, technoutopianism, The Fortune at the Bottom of the Pyramid, The Nature of the Firm, transaction costs

This stickiness could be the efficacy of a cluster of connections in pursuit of a goal one cares about, as in the case of the newly emerging peer-production enterprises. It could be the ways in which the internal social interaction has combined social norms with platform design to offer relatively stable relations with others who share common interests. Users do not amble around in a social equivalent of Brownian motion. They tend to cluster in new social relations, albeit looser and for more limited purposes than the traditional pillars of community. 667 The conceptual answer has been that the image of "community" that seeks a facsimile of a distant pastoral village is simply the wrong image of how we interact as social beings. We are a networked society now--networked individuals connected with each other in a mesh of loosely knit, overlapping, flat connections.


pages: 662 words: 180,546

Never Let a Serious Crisis Go to Waste: How Neoliberalism Survived the Financial Meltdown by Philip Mirowski

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Andrei Shleifer, asset-backed security, bank run, barriers to entry, Basel III, Berlin Wall, Bernie Madoff, Bernie Sanders, Black Swan, blue-collar work, Bretton Woods, Brownian motion, capital controls, Carmen Reinhart, Cass Sunstein, central bank independence, cognitive dissonance, collapse of Lehman Brothers, collateralized debt obligation, complexity theory, constrained optimization, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, crony capitalism, dark matter, David Brooks, David Graeber, debt deflation, deindustrialization, Edward Glaeser, Eugene Fama: efficient market hypothesis, experimental economics, facts on the ground, Fall of the Berlin Wall, financial deregulation, financial innovation, Flash crash, full employment, George Akerlof, Goldman Sachs: Vampire Squid, Hernando de Soto, housing crisis, Hyman Minsky, illegal immigration, income inequality, incomplete markets, invisible hand, Jean Tirole, joint-stock company, Kenneth Rogoff, knowledge economy, l'esprit de l'escalier, labor-force participation, liquidity trap, loose coupling, manufacturing employment, market clearing, market design, market fundamentalism, Martin Wolf, Mont Pelerin Society, moral hazard, mortgage debt, Naomi Klein, Nash equilibrium, night-watchman state, Northern Rock, Occupy movement, offshore financial centre, oil shock, payday loans, Ponzi scheme, precariat, prediction markets, price mechanism, profit motive, quantitative easing, race to the bottom, random walk, rent-seeking, Richard Thaler, road to serfdom, Robert Shiller, Robert Shiller, Ronald Coase, Ronald Reagan, savings glut, school choice, sealed-bid auction, Silicon Valley, South Sea Bubble, Steven Levy, technoutopianism, The Chicago School, The Great Moderation, the map is not the territory, The Myth of the Rational Market, the scientific method, The Wisdom of Crowds, theory of mind, Thomas Kuhn: the structure of scientific revolutions, Thorstein Veblen, Tobin tax, too big to fail, transaction costs, War on Poverty, Washington Consensus, We are the 99%, working poor

Let us look more closely at the practical mechanics of orthodox contemporary “economics imperialism.” While gleefully encroaching upon the spheres of interest of other disciplines, orthodox economics has also freely appropriated formalisms and methods from those other disciplines: think of the advent of “experimental economics” or the embrace of magnetic resonance imaging, or attempts to absorb chaos theory or nonstandard analysis or Brownian motion through the Ito calculus. Indeed, if there has been any conceptual constant throughout the history of neoclassical theory since the 1870s, it has been slavish attempts to slake its physics envy through gorging on half-digested imitations of physical models. A social science so promiscuous in its avidity to mimic the tools and techniques of other disciplines has no principled discrimination about what constitutes just and proper argumentation within its own sphere; and this has only become aggravated in the decades since 1980.


pages: 695 words: 219,110

The Fabric of the Cosmos by Brian Greene

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airport security, Albert Einstein, Albert Michelson, Arthur Eddington, Brownian motion, clockwork universe, conceptual framework, cosmic microwave background, cosmological constant, dark matter, dematerialisation, Hans Lippershey, Henri Poincaré, invisible hand, Isaac Newton, Murray Gell-Mann, Richard Feynman, Richard Feynman, Stephen Hawking, urban renewal

As we will see in Chapter 13, recent work in string theory has suggested that strings may be much larger than the Planck length, and this has a number of potentially critical implications—including the possibility of making the theory experimentally testable. 13. The existence of atoms was initially argued through indirect means (as an explanation of the particular ratios in which various chemical substances would combine, and later, through Brownian motion); the existence of the first black holes was confirmed (to many physicists’ satisfaction) by seeing their effect on gas that falls toward them from nearby stars, instead of “seeing” them directly. 14. Since even a placidly vibrating string has some amount of energy, you might wonder how it’s possible for a string vibrational pattern to yield a massless particle. The answer, once again, has to do with quantum uncertainty.


pages: 1,336 words: 415,037

The Snowball: Warren Buffett and the Business of Life by Alice Schroeder

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affirmative action, Albert Einstein, anti-communist, Ayatollah Khomeini, barriers to entry, Bonfire of the Vanities, Brownian motion, capital asset pricing model, card file, centralized clearinghouse, collateralized debt obligation, corporate governance, Credit Default Swap, credit default swaps / collateralized debt obligations, desegregation, Donald Trump, Eugene Fama: efficient market hypothesis, global village, Golden Gate Park, Haight Ashbury, haute cuisine, Honoré de Balzac, If something cannot go on forever, it will stop, In Cold Blood by Truman Capote, index fund, indoor plumbing, interest rate swap, invisible hand, Isaac Newton, Jeff Bezos, joint-stock company, joint-stock limited liability company, Long Term Capital Management, Louis Bachelier, margin call, market bubble, Marshall McLuhan, medical malpractice, merger arbitrage, Mikhail Gorbachev, moral hazard, NetJets, new economy, New Journalism, North Sea oil, paper trading, passive investing, pets.com, Plutocrats, plutocrats, Ponzi scheme, Ralph Nader, random walk, Ronald Reagan, Scientific racism, shareholder value, short selling, side project, Silicon Valley, Steve Ballmer, Steve Jobs, supply-chain management, telemarketer, The Predators' Ball, The Wealth of Nations by Adam Smith, Thomas Malthus, too big to fail, transcontinental railway, Upton Sinclair, War on Poverty, Works Progress Administration, Y2K, zero-coupon bond

“Billy Rogers Died of Drug Overdose,” Omaha World-Herald, April 2, 1987; “Cause Is Sought in Death of Jazz Guitarist Rogers,” Omaha World-Herald, February 21, 1987. 35. Interview with Arjay Miller. 36. Interviews with Verne McKenzie, Malcolm “Kim” Chace III, Don Wurster, Dick and Mary Holland. 37. Interview with George Brumley. 38. Louis Jean-Baptiste Alphonse Bachelier, Theory of Speculation, 1900. Bachelier applied the scientific theory of “Brownian motion” to the market, probably the first of many attempts to bring the rigor and prestige of hard science to the soft science of economics. 39. Charles Ellis, Investment Policy: How to Win the Loser’s Game. Illinois: Dow-Jones-Irwin, 1985, which is based on his article “Winning the Loser’s Game” in the July/August 1975 issue of the Financial Analysts Journal. 40. The modern-day equivalents of Tweedy Browne’s Jamaica Water warrants still exist, for example. 41.