| Preface |
| Introduction |
| Market Equilibrium / A.： |
| Equilibrium under Uncertainty / B.： |
| Security-Spot Market Equilibrium / C.： |
| State Pricing Model of Securities / D.： |
| Binomial Arbitrage Pricing Model of Securities / E.： |
| Capital Asset Pricing Model / F.： |
| Stochastic Control Pricing Model / G.： |
| The Potential-Price Matrix / H.： |
| Ito's Lemma--A Simple Case / I.： |
| Continuous-Time Portfolio Control / J.： |
| Black-Scholes Option Pricing Formula / K.： |
| Representative Agent Asset Pricing / L.： |
| Exercises |
| Notes |
| Static Economies / Chapter I.： |
| The Geometry of Choices and Prices / 1.： |
| Vector Spaces |
| Normed Spaces |
| Convexity and Cones |
| Function Spaces |
| Topology |
| Duality |
| Dual Representation |
| Preferences / 2.： |
| Preference Relations |
| Preference Continuity and Convexity |
| Utility Functions |
| Utility Representation |
| Quasi-Concave Utility |
| Monotonicity |
| Non-Satiation |
| Primitives of an Economy / 3.： |
| Equilibria |
| Exchange and Net Trade Economies |
| Production and Exchange Equilibria |
| Equilibrium and Efficiency |
| Efficiency and Equilibrium |
| Existence of Equilibria |
| First Probability Concepts / 4.： |
| Probability Spaces |
| Random Variables and Distributions |
| Measurability, Topology, and Partitions |
| Almost Sure Events and Versions |
| Expectation and Integration |
| Distribution and Density Functions |
| Expected Utility / 5.： |
| Von-Neumann-Morgenstern and Savage Models of Preferences |
| Expected Utility Representation |
| Preferences over Probability Distributions |
| Mixture Spaces and the Independence Axiom |
| Axioms for Expected Utility |
| Special Choice Spaces / 6.： |
| Banach Spaces |
| Measurable Function Spaces |
| L[superscript q] Spaces |
| L[superscript [infinity] Spaces |
| Riesz Representation |
| Continuity of Positive Linear Functionals |
| Hilbert Spaces |
| Portfolios / 7.： |
| Span and Vector Subspaces |
| Linearly Independent Bases |
| Equilibrium on a Subspace |
| Security Market Equilibria |
| Constrained Efficiency |
| Optimization Principles / 8.： |
| First Order Necessary Conditions |
| Saddle Point Theorem |
| Kuhn-Tucker Theorem |
| Superdifferentials and Maxima |
| Second Probability Concepts / 9.： |
| Changing Probabilities |
| Changing Information |
| Conditional Expectation |
| Properties of Conditional Expectation |
| Expectation in General Spaces |
| Jensen's Inequality |
| Independence and The Law of Large Numbers |
| Risk Aversion / 10.： |
| Defining Risk Aversion |
| Risk Aversion and Concave Expected Utility |
| Risk Aversion and Second Order Stochastic Dominance |
| Equilibrium in Static Markets Under Uncertainty / 11.： |
| Markets for Assets with a Variance |
| Beta Models: Mean-Covariance Pricing |
| The CAPM and APT Pricing Approaches |
| Variance Aversion |
| The Capital Asset Pricing Model |
| Proper Preferences |
| Stochastic Economies / Chapter II.： |
| Event Tree Economies / 12.： |
| Event Trees |
| Security and Spot Markets |
| Trading Strategies |
| Marketed Subspaces and Tight Markets |
| Dynamic and Static Equilibria |
| Dynamic Spanning and Complete Markets |
| A Security Valuation Operator |
| Dynamically Complete Markets Equilibria |
| Dynamically Incomplete Markets Equilibria |
| Generic Existence of Equilibria with Real Securities |
| Arbitrage Security Valuation and State Prices |
| A Dynamic Theory of the Firm / 13.： |
| Stock Market Equilibria |
| An Example |
| Security Trading by Firms |
| Invariance of Stock Values to Security Trading by Firms |
| Modigliani-Miller Theorem |
| Invariance of Firm's Total Market Value Process |
| Firms Issue and Retire Securities |
| Tautology of Complete Information Models |
| The Goal of the Firm |
| Stochastic Processes / 14.： |
| The Information Filtration |
| Informationally Adapted Processes |
| Information Generated by Processes and Event Trees |
| Technical Continuity Conditions |
| Martingales |
| Brownian Motion and Poisson Processes |
| Stopping Times, Local Martingales, and Semimartingales |
| Stochastic Integrals and Gains From Security Trade / 15.： |
| Discrete-Time Stochastic Integrals |
| Continuous-Time Primitives |
| Simple Continuous-Time Integration |
| The Stochastic Integral |
| General Stochastic Integrals |
| Martingale Multiplicity |
| Stochastic Integrals and Changes of Probability |
| Stochastic Equilibria / 16.： |
| Dynamic Spanning |
| Transformations to Martingale Gains from Trade / 17.： |
| Introduction: The Finite-Dimensional Case |
| Dividend and Price Processes |
| Self-Financing Trading Strategies |
| Representation of Implicit Market Values |
| Equivalent Martingale Measures |
| Choice of Numeraire |
| A Technicality |
| Generalization to Many Goods |
| Generalization to Consumption Through Time |
| Discrete-Time Asset Pricing / Chapter III.： |
| Markov Processes and Markov Asset Valuation / 18.： |
| Markov Chains |
| Transition Matrices |
| Metric and Borel Spaces |
| Conditional and Marginal Distributions |
| Markov Transition |
| Transition Operators |
| Chapman-Kolmogorov Equation |
| Sub-Markov Transition |
| Markov Arbitrage Valuation |
| Abstract Markov Process |
| Discrete-Time Markov Control / 19.： |
| Robinson Crusoe Example |
| Dynamic Programming with a Finite State Space |
| Borel-Markov Control Models |
| Existence of Stationary Markov Optimal Control |
| Measurable Selection of Maxima |
| Bellman Operator |
| Contraction Mapping and Fixed Points |
| Bellman Equation |
| Finite Horizon Markov Control |
| Stochastic Consumption and Investment Control |
| Discrete-Time Equilibrium Pricing / 20.： |
| Markov Exchange Economies |
| Optimal Portfolio and Consumption Policies |
| Conversion to a Borel-Markov Control Problem |
| Markov Equilibrium Security Prices |
| Relaxation of Short-Sales Constraints |
| Markov Production Economies |
| A Central Planning Stochastic Production Problem |
| Market Decentralization of a Growth Economy |
| Markov Stock Market Equilibrium |
| Continuous-Time Asset Pricing / Chapter IV.： |
| An Overview of the Ito Calculus / 21.： |
| Ito Processes and Integrals |
| Ito's Lemma |
| Stochastic Differential Equations |
| Feynman-Kac Formula |
| Girsanov's Theorem: Change of Probability and Drift |
| The Black-Scholes Model of Security Valuation / 22.： |
| Binomial Pricing Model |
| Black-Scholes Framework |
| Reduction to a Partial Differential Equation |
| The Black-Scholes Option Pricing Formula |
| An Application of the Feynman-Kac Formula |
| An Extension |
| Central Limit Theorems |
| Limiting Binomial Formula |
| Uniform Integrability |
| An Application of Donsker's Theorem |
| An Application of Girsanov's Theorem |
| An Introduction to the Control of Ito Processes / 23.： |
| Sketch of Bellman's Equation |
| Regularity Requirements |
| Formal Statement of Bellman's Equation |
| Portfolio Choice with I.I.D. Returns / 24.： |
| The Portfolio Control Problem |
| The Solution |
| Continuous-Time Equilibrium Asset Pricing / 25.： |
| The Setting |
| Definition of Equilibrium |
| Regularity Conditions |
| Equilibrium Theorem |
| Conversion to Consumption Numeraire |
| Equilibrium Interest Rates |
| The Consumption-Based Capital Asset Pricing Model |
| The Cox-Ingersoll-Ross Term Structure Model |
| Bibliography |
| Author Index |
| Symbol Glossary |
| Subject Index |
図書
