Stochastic Optimization Models in Finance

PrefaceAcknowledgmentsPart I. Mathematical Tools Introduction 1. Expected Utility Theory A General Theory of Subjective Probabilities and Expected Utilities 2. Convexity and the Kuhn-Tucker Conditions Pseudo-Convex Functions Convexity, Pseudo-Convexity and Quasi-Convexity of Composite Functions 3. Dynamic Programming Introduction to Dynamic Programming Computational and Review Exercises Mind-Expanding ExercisesPart II. Qualitative Economic Results Introduction 1. Stochastic Dominance The Efficiency Analysis of Choices Involving Risk A Unified Approach to Stochastic Dominance 2. Measures of Risk Aversion Risk Aversion in the Small and in the Large 3. Separation Theorems The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets Separation in Portfolio Analysis Computational and Review Exercises Mind-Expanding ExercisesPart III. Static Portfolio Selection Models Introduction 1. Mean-Variance and Safety First Approaches and Their Extensions The Fundamental Approximation Theorem of Portfolio Analysis in Terms of Means, Variances and Higher Moments The Asymptotic Validity of Quadratic Utility as the Trading Interval Approaches Safety-First and Expected Utility Maximization in Mean-Standard Deviation Portfolio Analysis Choosing Investment Portfolios When the Returns have Stable Distributions 2. Existence and Diversification of Optimal Portfolio Policies On the Existence of Optimal Policies Under Uncertainty General Proof That Diversification Pays 3. Effects of Taxes on Risk Taking The Effects of Income, Wealth, and Capital Gains Taxation on Risk-Taking Some Effects of Taxes on Risk-Taking Computational and Review Exercises Mind-Expanding ExercisesPart IV. Dynamic Models Reducible to Static Models Introduction 1. Models that have a Single Decision Point Investment Analysis Under Uncertainty 2. Risk Aversion Over Time Implies Static Risk Aversion Multiperiod Consumption-Investment Decisions 3. Myopic Portfolio Policies On Optimal Myopic Portfolio Policies, with and without Serial Correlation of Yields Computational and Review Exercises Mind-Expanding ExercisesPart V. Dynamic Models Introduction Appendix A. An Intuitive Outline of Stochastic Differential Equations and Stochastic Optimal Control 1. Two-Period Consumption Models and Portfolio Revision Consumption Decisions Under Uncertainty A Dynamic Model for Bond Portfolio Management 2. Models of Optimal Capital Accumulation and Portfolio Selection Multiperiod Consumption-Investment Decisions and Risk Preference Lifetime Portfolio Selection by Dynamic Stochastic Programming Optimal Investment and Consumption Strategies Under Risk for a Class of Utility Functions 3. Models of Option Strategy The Value of the Call Option on a Bond Evaluating a Call Option and Optimal Timing Strategy in the Stock Market Bond Refunding with Stochastic Interest Rates Minimax Policies for Selling an Asset and Dollar Averaging 4. The Capital Growth Criterion and Continuous-Time Models Investment Policies for Expanding Businesses Optimal in a Long-Run Sense Portfolio Choice and the Kelly Criterion Optimum Consumption and Portfolio Rules in a Continuous-Time Model Computational and Review Exercises Mind-Expanding ExercisesBibliographyIndex