1 The moving target 1
1.1 Invariance principles and laws of nature 1
1.2 Humanly invented law can always be violated 3
1.3 Where are we headed? 6
2 Neo-classical economic theory 9
2.1 Why study"optimizing behavior"? 9
2.2 Dissecting neo-classical economic theory(microeconomics) 10
2.3 The myth of equilibrium via perfect information 16
2.4 How many green jackets does a consumer want? 21
2.5 Macroeconomic lawlessness 22
2.6 When utility doesn't exist 26
2.7 Global perspectives in economics 28
2.8 Local perspectives in physics 29
3 Probability and stochastic processes 31
3.1 Elementary rules of probability theory 31
3.2 The empirical distribution 32
3.3 Some properties of probability distributions 33
3.4 Some theoretical distributions 35
3.5 Laws of large numbers 38
3.6 Stochastic processes 41
3.7 Correlations and stationary processes 58
4 Scaling the ivory tower of finance 63
4.1 Prolog 63
4.2 Horse trading by a fancy name 63
4.3 Liquidity,and several shaky ideas of"true value" 64
4.4 The Gambler's Ruin 67
4.5 The Modigliani-Miller argument 68
4.6 From Gaussian returns to fat tails 72
4.7 The best tractable approximation to liquid market dynamics 75
4.8 "Temporary price equilibria"and other wrong ideas of"equilibrium"in economics and finance 76
4.9 Searching for Adam Smith's Invisible Hand 77
4.10 Black's"equilibrium":dreams of"springs"in the market 83
4.11 Macroeconomics:lawless phenomena? 85
4.12 No universal scaling exponents either! 86
4.13 Fluctuations,fat tails,and diversification 88
5 Standard betting procedures in portfolio selection theory 91
5.1 Introduction 91
5.2 Risk and return 91
5.3 Diversification and correlations 93
5.4 The CAPM portfolio selection strategy 97
5.5 The efficient market hypothesis 101
5.6 Hedging with options 102
5.7 Stock shares as options on a firm's assets 105
5.8 The Black-Scholes model 107
5.9 The CAPM option pricing strategy 109
5.10 Backward-time diffusion:solving the Black-Scholes pde 112
5.11 We can learn from Enron 118
6 Dynamics of financial markets,volatility,and option pricing 121
6.1 An empirical model of option pricing 121
6.2 Dynamics and volatility of returns 132
6.3 Option pricing via stretched exponentials 144
Appendix A.The first Kolmogorov equation 145
7 Thermodynamic analogies vs instability of markets 147
7.1 Liquidity and approximately reversible trading 147
7.2 Replicating self-financing hedges 148
7.3 Why thermodynamic analogies fail 150
7.4 Entropy and instability of financial markets 153
7.5 The challenge:to find at least one stable market 157
Appendix B.Stationary vs nonstationary random forces 157
8 Scaling,correlations,and cascades in finance and turbulence 161
8.1 Fractal vs self-affine scaling 161
8.2 Persistence and antipersistence 163
8.3 Martingales and the efficient market hypothesis 166
8.4 Energy dissipation in fluid turbulence 169
8.5 Multiaffine scaling in turbulence models 173
8.6 Levy distributions 176
8.7 Recent analyses of financial data 179
Appendix C.Continuous time Markov processes 184
9 What is complexity? 185
9.1 Patterns hidden in statistics 186
9.2 Computable numbers and functions 188
9.3 Algorithmic complexity 188
9.4 Automata 190
9.5 Chaos vs randomness vs complexity 192
9.6 Complexity at the border of chaos 193
9.7 Replication and mutation 195
9.8 Why not econobiology? 196
9.9 Note added April 8,2003 199
References 201
Index 207