Preface PART Ⅰ DISCRETE-TIME MODELS 1 Introduction to State Pricing A Arbitrage and State Prices B Risk-Neutral Probabilities C Optimality and Asset Pricing D Efficiency and Complete Markets E Optimality and Representative Agents F State-Price Beta Models Exercises Notes 2 The Basic Multiperiod Model A Uncertainty B Security Markets C Arbitrage, State Prices, and Martingales D Individual Agent Optimality E Equilibrium and Pareto Optimality. F Equilibrium Asset Pricing G Arbitrage and Martingale Measures H Valuation of Redundant Securities I American Exercise Policies and Valuation j is Early Exercise Optimal? Exercises Notes 3 The Dynamic Programming Approach A The Bellman Approach B First-Order Bellman Conditions C Markov Uncertainty D Markov Asset Pricing E Security Pricing by Markov Control F Markov Arbitrage-Free Valuation G Early Exercise and Optimal Stopping Exercises Notes 4 The Infinite-Horizon Setting A Markov Dynamic Programming B Dynamic Programming and Equilibrium C Arbitrage and State Prices D Optimality and State Prices E Method-of-Moments Estimation Exercises Notes PART Ⅱ CONTINUOUS-TIME MODELS 5 The Black-Scholes Model A Trading Gains for Brownian Prices B Martingale Trading Gains C Ito Prices and Gains D Ito's Formula E The Black-Scholes Option-Pricing Formula F Black-Scholes Formula: First Try G The PDE for Arbitrage-Free Prices H The Feynman-Kac Solution I The Multidimensional Case Exercises Notes 6 State Prices and Equivalent Martingale Measures A Arbitrage B Numeraire Invariance C State Prices and Doubling Strategies D Expected Rates of Return …… 7 Term-Structure Models 8 Derivative Pricing 9 Portfolio and Consumption Choice 10 Equilibrium 11 Comrporate Securities 12 Numerical Methods APPENDIXES
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