Asset pricing theory

Preface

Notation and Conventions

Part 1. Single-Period Analysis

Chapter 1. Financial Market and Arbitrage

1.1. Market and Arbitrage

1.2. Present Value and State Prices

1.3. Market Completeness and Dominant Choice

1.4. Probabilistic Representations of Value

1.5. Financial Contracts and Portfolios

1.6. Returns

1.7. Trading Constraints

1.8. Exercises

1.9. Notes

Chapter 2. Mean-Variance Analysis

2.1. Market and Inner Product Structure

2.2. Minimum-Variance Cash Flows

2.3. Minimum-Variance Returns

2.4. Beta Pricing

2.5. Sharpe Ratios

2.6. Mean-Variance Efficiency

2.7. Factor Pricing

2.8. Exercises

2.9. Notes

Chapter 3. Optimality and Equilibrium

3.1. Preferences, Optimality and State Prices

3.2. Equilibrium

3.3. Effective Market Completeness

3.4. Representative-Agent Pricing

3.4.1. Aggregation Based on Scale Invariance

3.4.2. Aggregation Based on Translation Invariance

3.5. Utility

3.5.1. Compensation Function Construction of Utilities

3.5.2. Additive Utilities

3.6. Utility and Individual Optimality

3.7. Utility and Allocational Optimality

3.8. Exercises

3.9. Notes

Chapter 4. Risk Aversion

4.1. Absolute and Comparative Risk Aversion

4.2. Expected Utility

4.3. Expected Utility and Risk Aversion

4.3.1. Comparative Risk Aversion

4.3.2. Absolute Risk Aversion

4.4. Risk Aversion and Simple Portfolio Choice

4.5. Coefficients of Risk Aversion

4.6. Simple Portfolio Choice for Small Risks

4.7. Stochastic Dominance

4.8. Exercises

4.9. Notes

Part 2. Discrete Dynamics

Chapter 5. Dynamic Arbitrage Pricing

5.1. Dynamic Market and Present Value

5.1.1. Time-Zero Market and Present-Value Functions

5.1.2. Dynamic Market and Present-Value Functions

5.2. Financial Contracts

5.2.1. Basic Arbitrage Restrictions and Trading Strategies

5.2.2. Budget Equations and Synthetic Contracts

5.3. Probabilistic Representations of Value

5.3.1. State-Price Densities

5.3.2. Equivalent Martingale Measures

5.4. Dominant Choice and Option Pricing

5.4.1. Dominant Choice

5.4.2. Recursive Value Maximization

5.4.3. Arbitrage Pricing of Options

5.5. State-Price Dynamics

5.6. Market Implementation

5.7. Markovian Pricing

5.8. Exercises

5.9. Notes

Chapter 6. Dynamic Optimality and Equilibrium

6.1. Dynamic Utility

6.2. Expected Discounted Utility

6.3. Recursive Utility

6.4. Basic Properties of Recursive Utility

6.4.1. Comparative Risk Aversion

6.4.2. Utility Gradient Density

6.4.3. Concavity

6.5. Scale/Translation Invariance

6.5.1. Scale-Invariant Kreps-Porteus Utility

6.5.2. Translation-Invariant Kreps-Porteus Utility

6.6. Equilibrium Pricing

6.6.1. Intertemporal Marginal Rate of Substitution

6.6.2. State Pricing with SI Kreps-Porteus Utility

6.6.3. State Pricing with TI Kreps-Porteus Utility

6.7. Optimal Consumption and Portfolio Choice

6.7.1. Generalities

6.7.2. Scale-Invariant Formulation

6.7.3. Translation-Invariant Formulation

6.8. Exercises

6.9. Notes

Part 3. Mathematical Background

Appendix A. Optimization Principles

A.1. Vector Space

A.2. Inner Product

A.3. Norm

A.4. Continuity

A.5. Compactness

A.6. Projections

A.7. Supporting Hyperplanes

A.8. Global Optimality Conditions

A.9. Local Optimality Conditions

A.10. Exercises

A.11. Notes

Appendix B. Discrete Stochastic Analysis

B.1. Events, Random Variables, Expectation

B.2. Algebras and Measurability

B.3. Conditional Expectation

B.4. Stochastic Independence

B.5. Filtration, Stopping Times and Stochastic Processes

B.6. Martingales

B.7. Predictable Martingale Representation

B.8. Change of Measure and Martingales

B.9. Markov Processes

B.10. Exercises

B.11. Notes

Bibliography

Index