Asset Pricing Theory

Asset Pricing Theoryis an advanced textbook for doctoral students and researchers that offers a modern introduction to the theoretical and methodological foundations of competitive asset pricing. Costis Skiadas develops in depth the fundamentals of arbitrage pricing, mean-variance analysis, equilibrium pricing, and optimal consumption/portfolio choice in discrete settings, but with emphasis on geometric and martingale methods that facilitate an effortless transition to the more advanced continuous-time theory.Among the book's many innovations are its use of recursive utility as the benchmark representation of dynamic preferences, and an associated theory of equilibrium pricing and optimal portfolio choice that goes beyond the existing literature.Asset Pricing Theoryis complete with extensive exercises at the end of every chapter and comprehensive mathematical appendixes, making this book a self-contained resource for graduate students and academic researchers, as well as mathematically sophisticated practitioners seeking a deeper understanding of concepts and methods on which practical models are built. Covers in depth the modern theoretical foundations of competitive asset pricing and consumption/portfolio choice Uses recursive utility as the benchmark preference representation in dynamic settings Sets the foundations for advanced modeling using geometric arguments and martingale methodology Features self-contained mathematical appendixes Includes extensive end-of-chapter exercises

Preface	p. xi
Notation and Conventions	p. xv
Single-Period Analysis
Financial Market and Arbitrage	p. 3
Market and Arbitrage	p. 3
Present Value and State Prices	p. 6
Market Completeness and Dominant Choice	p. 9
Probabilistic Representations of Value	p. 12
Financial Contracts and Portfolios	p. 15
Returns	p. 17
Trading Constraints	p. 19
Exercises	p. 22
Notes	p. 27
Mean-Variance Analysis	p. 29
Market and Inner Product Structure	p. 29
Minimum-Variance Cash Flows	p. 32
Minimum-Variance Returns	p. 35
Beta Pricing	p. 37
Sharpe Ratios	p. 40
Mean-Variance Efficiency	p. 43
Factor Pricing	p. 46
Exercises	p. 49
Notes	p. 54
Optimality and Equilibrium	p. 55
Preferences, Optimality and State Prices	p. 55
Equilibrium	p. 58
Effective Market Completeness	p. 62
Representative-Agent Pricing	p. 65
Aggregation Based on Scale Invariance	p. 66
Aggregation Based on Translation Invariance	p. 69
Utility	p. 71
Compensation Function Construction of Utilities	p. 72
Additive Utilities	p. 76
Utility and Individual Optimality	p. 79
Utility and Allocational Optimality	p. 83
Exercises	p. 87
Notes	p. 91
Risk Aversion	p. 94
Absolute and Comparative Risk Aversion	p. 94
Expected Utility	p. 99
Expected Utility and Risk Aversion	p. 103
Comparative Risk Aversion	p. 103
Absolute Risk Aversion	p. 105
Risk Aversion and Simple Portfolio Choice	p. 109
Coefficients of Risk Aversion	p. 112
Simple Portfolio Choice for Small Risks	p. 116
Stochastic Dominance	p. 120
Exercises	p. 124
Notes	p. 129
Discrete Dynamics
Dynamic Arbitrage Pricing	p. 135
Dynamic Market and Present Value	p. 135
Time-Zero Market and Present-Value Functions	p. 135
Dynamic Market and Present-Value Functions	p. 138
Financial Contracts	p. 142
Basic Arbitrage Restrictions and Trading Strategies	p. 142
Budget Equations and Synthetic Contracts	p. 146
Probabilistic Representations of Value	p. 150
State-Price Densities	p. 150
Equivalent Martingale Measures	p. 154
Dominant Choice and Option Pricing	p. 159
Dominant Choice	p. 160
Recursive Value Maximization	p. 164
Arbitrage Pricing of Options	p. 166
State-Price Dynamics	p. 170
Market Implementation	p. 174
Markovian Pricing	p. 178
Exercises	p. 183
Notes	p. 193
Dynamic Optimality and Equilibrium	p. 195
Dynamic Utility	p. 195
Expected Discounted Utility	p. 199
Recursive Utility	p. 202
Basic Properties of Recursive Utility	p. 206
Comparative Risk Aversion	p. 206
Utility Gradient Density	p. 208
Concavity	p. 211
Scale/Translation Invariance	p. 213
Scale-Invariant Kreps-Porteus Utility	p. 213
Translation-Invariant Kreps-Porteus Utility	p. 217
Equilibrium Pricing	p. 219
Intertemporal Marginal Rate of Substitution	p. 220
State Pricing with SI Kreps-Porteus Utility	p. 221
State Pricing with TI Kreps-Porteus Utility	p. 227
Optimal Consumption and Portfolio Choice	p. 229
Generalities	p. 230
Scale-Invariant Formulation	p. 232
Translation-Invariant Formulation	p. 240
Exercises	p. 248
Notes	p. 252
Mathematical Background
Optimization Principles	p. 259
Vector Space	p. 259
Inner Product	p. 261
Norm	p. 264
Continuity	p. 266
Compactness	p. 268
Projections	p. 270
Supporting Hyperplanes	p. 274
Global Optimality Conditions	p. 276
Local Optimality Conditions	p. 278
Exercises	p. 281
Notes	p. 284
Discrete Stochastic Analysis	p. 285
Events, Random Variables, Expectation	p. 285
Algebras and Measurability	p. 289
Conditional Expectation	p. 292
Stochastic Independence	p. 296
Filtration, Stopping Times and Stochastic Processes	p. 299
Martingales	p. 304
Predictable Martingale Representation	p. 308
Change of Measure and Martingales	p. 312
Markov Processes	p. 317
Exercises	p. 320
Notes	p. 324
Bibliography	p. 327
Index	p. 341
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