Stochastic Optimization Models in Finance

Preface

Acknowledgments

Part 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 Exercises

Part 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 Exercises

Part 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 Exercises

Part 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 Exercises

Part 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 Exercises

Bibliography

Index