Economic and Financial Decisions under Risk

Preface ix I: Decision Theory 1 Chapter 1: Risk Aversion 3 1.1 An Historical Perspective on Risk Aversion 3 1.2 Definition and Characterization of Risk Aversion 7 1.3 Risk Premium and Certainty Equivalent 9 1.4 Degree of Risk Aversion 13 1.5 Decreasing Absolute Risk Aversion and Prudence 16 1.6 Relative Risk Aversion 17 1.7 Some Classical Utility Functions 19 1.8 Bibliographical References, Extensions and Exercises 22 Chapter 2: The Measures of Risk 27 2.1 Increases in Risk 28 2.2 Aversion to Downside Risk 36 2.3 First-Degree Stochastic Dominance 37 2.4 Bibliographical References, Extensions and Exercises 39 II Risk Management 43 Chapter 3: Insurance Decisions 45 3.1 Optimal Insurance: an Illustration 47 3.2 Optimal Coinsurance 49 3.3 Comparative Statics in the Coinsurance Problem 53 3.4 The Optimality of Deductible Insurance 56 3.5 Bibliographical References, Extensions and Exercises 59 Chapter 4: Static Portfolio Choices 65 4.1 The One-Risky-One-Riskfree-Asset Model 65 4.2 The Effect of Background Risk 684.3 Portfolios of Risky Assets 70 4.4 Bibliographical References, Extensions and Exercises 74 Chapter 5: Static Portfolio Choices in an Arrow-Debreu Economy 77 5.1 Arrow-Debreu Securities and Arbitrage Pricing 78 5.2 Optimal Portfolios of Arrow-Debreu Securities 80 5.3 A Simple Graphical Illustration 83 5.4 Bibliographical References, Extensions and Exercises 85 Chapter 6: Consumption and Saving 89 6.1 Consumption and Saving under Certainty 89 6.2 Uncertainty and Precautionary Savings 95 6.3 Risky Savings and Precautionary Demand 98 6.4 Time Consistency 99 6.5 Bibliographical References, Extensions and Exercises 101 Chapter 7: Dynamic Portfolio Management 107 7.1 Backward Induction 108 7.2 The Dynamic Investment Problem 109 7.3 Time Diversification 113 7.4 Portfolio Management with Predictable Returns 114 7.5 Learning about the Distribution of Excess Returns 117 7.6 Bibliographical References, Extensions and Exercises 119 Chapter 8: Risk and Information 123 8.1 The Value of Information 123 8.2 Comparative Statics Analysis 130 8.3 The Hirshleifer Effect 134 8.4 Bibliographical References, Extensions and Exercises 136 Chapter 9: Optimal Prevention 141 9.1 Prevention under Risk Neutrality 142 9.2 Risk Aversion and Optimal Prevention 142 9.3 Prudence and Optimal Prevention 144 9.4 Bibliographical References, Extensions and Exercises 145 III Risk Sharing 151 Chapter 10: Efficient Allocations of Risks 153 10.1 Risk Sharing: an Illustration 153 10.2 Description of the Economy and Definition 155 10.3 Characterization of Efficient Allocations of Risk 157 10.4 Aggregation of Preferences 163 10.5 Bibliographical References, Extensions and Exercises 165 Chapter 11: Asset Pricing 169 11.1 Competitive Markets for Arrow-Debreu Securities 169 11.2 The First Theorem of Welfare Economics 170 11.3 The Equity Premium 17211.4 The Capital Asset-Pricing Model 175 11.5 Two-Fund Separation Theorem 177 11.6 Bond Pricing 179 11.7 Bibliographical References, Extensions and Exercises 184 IV Extensions 189 Chapter 12: Asymmetric Information 191 12.1 Adverse Selection 192 12.2 Moral Hazard 199 12.3 The Principal-Agent Problem 203 12.4 Bibliographical References, Extensions and Exercises 209 Chapter 13: Alternative Decision Criteria 213 13.1 The Independence Axiom and the Allais Paradox 215 13.2 Rank-Dependent EU 217 13.3 Ambiguity Aversion 221 13.4 Prospect Theory and Loss Aversion 224 13.5 Some Concluding Thoughts 226 13.6 Bibliographical References, Extensions and Exercises 227 Index 231