The Economics of Risk and Time / Edition 1 available in Paperback
The Economics of Risk and Time / Edition 1
- ISBN-10:
- 0262572249
- ISBN-13:
- 9780262572248
- Pub. Date:
- 08/20/2004
- Publisher:
- MIT Press
- ISBN-10:
- 0262572249
- ISBN-13:
- 9780262572248
- Pub. Date:
- 08/20/2004
- Publisher:
- MIT Press
The Economics of Risk and Time / Edition 1
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Overview
The book covers these topics: expected utility theory and related concepts; the standard portfolio problem of choice under uncertainty involving two different assets; P the basic hyperplane separation theorem and log-supermodular functions as technical tools for solving various decision-making problems under uncertainty; s choice involving multiple risks; the Arrow-Debreu portfolio problem; consumption and saving; the equilibrium price of risk and time in an Arrow-Debreu economy; and dynamic models of decision making when a flow of information on future risks is expected over time. The book is appropriate for both students and professionals. Concepts are presented intuitively as well as formally, and the theory is balanced by empirical considerations. Each chapter concludes with a problem set.
Product Details
| ISBN-13: | 9780262572248 |
|---|---|
| Publisher: | MIT Press |
| Publication date: | 08/20/2004 |
| Series: | The MIT Press |
| Edition description: | New Edition |
| Pages: | 466 |
| Product dimensions: | 5.94(w) x 9.00(h) x 0.92(d) |
| Age Range: | 18 Years |
About the Author
Christian Gollier is Professor of Economics at the University of Toulouse, FFSA Chair of Insurance at the Institut d'Economie Industrielle, and coordinator of the European area network in Applied Microeconomics at CESifo.
Table of Contents
| Preface | xv | |
| Acknowledgments | xix | |
| I | General Theory | 1 |
| 1 | The Expected Utility Model | 3 |
| 1.1 | Simple and Compound Lotteries | 3 |
| 1.2 | Axioms on Preferences under Uncertainty | 4 |
| 1.3 | The Expected Utility Theorem | 6 |
| 1.4 | Critics of the Expected Utility Model | 9 |
| 1.4.1 | The Allais Paradox | 10 |
| 1.4.2 | The Allais Paradox and Time Consistency | 11 |
| 2 | Risk Aversion | 17 |
| 2.1 | Characterization of Risk Aversion | 17 |
| 2.2 | Comparative Risk Aversion | 18 |
| 2.3 | Certainty Equivalent and Risk Premium | 20 |
| 2.4 | The Arrow-Pratt Approximation | 21 |
| 2.5 | Decreasing Absolute Risk Aversion | 24 |
| 2.6 | Some Classical Utility Functions | 25 |
| 2.7 | Test for Your Own Degree of Risk Aversion | 29 |
| 2.8 | An Application: The Cost of Macroeconomic Risks | 32 |
| 3 | Change in Risk | 39 |
| 3.1 | The Extremal Approach | 40 |
| 3.2 | Second-Order Stochastic Dominance | 42 |
| 3.3 | Diversification | 45 |
| 3.4 | First-Order Stochastic Dominance | 46 |
| II | The Standard Portfolio Problem | 51 |
| 4 | The Standard Portfolio Problem | 53 |
| 4.1 | The Model and Its Basic Properties | 53 |
| 4.2 | The Case of a Small Risk | 55 |
| 4.3 | The Case of HARA Functions | 57 |
| 4.4 | The Impact of Risk Aversion | 58 |
| 4.5 | The Impact of a Change in Risk | 59 |
| 5 | The Equilibrium Price of Risk | 65 |
| 5.1 | A Simple Equilibrium Model for Financial Markets | 65 |
| 5.2 | The Equity Premium Puzzle | 68 |
| 5.3 | The Equity Premium with Limited Participation | 71 |
| 5.4 | The Equity Premium and the Integration of International Financial Markets | 73 |
| III | Some Technical Tools and Their Applications | 79 |
| 6 | A Hyperplane Separation Theorem | 81 |
| 6.1 | The Diffidence Theorem | 81 |
| 6.2 | Link with the Jensen's Inequality | 88 |
| 6.3 | Applications of the Diffidence Theorem | 89 |
| 6.3.1 | Diffidence | 89 |
| 6.3.2 | Comparative Diffidence | 90 |
| 6.3.3 | Central Risk Aversion | 91 |
| 6.3.4 | Central Riskiness | 92 |
| 6.4 | The Covariance Rule | 94 |
| 7 | Log-Supermodularity | 99 |
| 7.1 | Definition | 99 |
| 7.2 | Log-Supermodularity and Single Crossing | 102 |
| 7.2.1 | A Theoretical Result | 102 |
| 7.2.2 | Applications to the Standard Portfolio Problem | 103 |
| 7.2.3 | Jewitt's Preference Orders | 104 |
| 7.3 | Expectation of a Log-Supermodular Function | 105 |
| 7.3.1 | A Theoretical Result | 105 |
| 7.3.2 | Two Applications | 106 |
| IV | Multiple Risks | 111 |
| 8 | Risk Aversion with Background Risk | 113 |
| 8.1 | Preservation of DARA | 114 |
| 8.2 | The Comparative Risk Aversion Is Not Preserved | 117 |
| 8.3 | Extensions with Dependent Background Risk | 119 |
| 8.3.1 | Affiliated Background Risk | 119 |
| 8.3.2 | The Comparative Risk Aversion in the Sense of Ross | 121 |
| 9 | The Tempering Effect of Background Risk | 125 |
| 9.1 | Risk Vulnerability | 126 |
| 9.2 | Risk Vulnerability and Increase in Risk | 130 |
| 9.2.1 | Increase in Background Risk | 130 |
| 9.2.2 | Increase in the Endogenous Risk | 130 |
| 9.3 | Risk Vulnerability and the Equity Premium Puzzle | 131 |
| 9.4 | Generalized Risk Vulnerability | 132 |
| 9.5 | Standardness | 135 |
| 10 | Taking Multiple Risks | 141 |
| 10.1 | The Interaction between Asset Demand and Small Gambles | 142 |
| 10.2 | Are Independent Assets Substitutes? | 144 |
| 10.2.1 | The i.i.d. Case | 144 |
| 10.2.2 | The General Case | 150 |
| 11 | The Dynamic Investment Problem | 155 |
| 11.1 | Static versus Dynamic Optimization | 157 |
| 11.2 | The Standard Portfolio Problem | 158 |
| 11.2.1 | The Model | 158 |
| 11.2.2 | The HARA Case | 160 |
| 11.2.3 | A Sufficient Condition for Younger People to Be More Risk-Averse | 161 |
| 11.3 | Discussion of the Results | 165 |
| 11.3.1 | Nonlinear Risk Tolerance | 165 |
| 11.3.2 | Nondifferentiable Marginal Utility | 166 |
| 11.4 | Background Risk and Time Horizon | 168 |
| 11.4.1 | Investors Bear a Background Risk at Retirement | 168 |
| 11.4.2 | Stationary Income Process | 171 |
| 12 | Special Topics in Dynamic Finance | 175 |
| 12.1 | The Length of Periods between Trade | 175 |
| 12.2 | Dynamic Discrete Choice | 179 |
| 12.3 | Constraints on Feasible Strategies | 183 |
| 12.4 | The Effect of a Leverage Constraint | 185 |
| 12.4.1 | The Case of a Lower Bound on the Investment in the Risky Asset | 185 |
| 12.4.2 | The Case of an Upper Bound on the Investment in the Risky Asset | 187 |
| V | The Arrow-Debreu Portfolio Problem | 193 |
| 13 | The Demand for Contingent Claims | 195 |
| 13.1 | The Model | 196 |
| 13.2 | Characterization of the Optimal Portfolio | 197 |
| 13.3 | The Impact of Risk Aversion | 200 |
| 14 | Risk on Wealth | 205 |
| 14.1 | The Marginal Propensity to Consume in State [pi] | 206 |
| 14.2 | The Preservation of DARA and IARA | 208 |
| 14.3 | The Marginal Value of Wealth | 210 |
| 14.4 | Aversion to Risk on Wealth | 211 |
| VI | Consumption and Saving | 215 |
| 15 | Consumption under Certainty | 217 |
| 15.1 | Time Separability | 217 |
| 15.2 | Exponential Discounting | 218 |
| 15.3 | Consumption Smoothing under Certainty | 219 |
| 15.4 | Analogy with the Portfolio Problem | 221 |
| 15.5 | The Social Cost of Volatility | 224 |
| 15.6 | The Marginal Propensity to Consume | 226 |
| 15.7 | Time Diversification and Self-Insurance | 227 |
| 16 | Precautionary Saving and Prudence | 235 |
| 16.1 | Prudence | 235 |
| 16.2 | The Demand for Saving | 239 |
| 16.3 | The Marginal Propensity to Consume under Uncertainty | 239 |
| 16.3.1 | Does Uncertainty Increase the MPC? | 240 |
| 16.3.2 | Does Uncertainty Make the MPC Decreasing in Wealth? | 241 |
| 16.4 | More Than Two Periods | 242 |
| 16.4.1 | The Euler Equation | 242 |
| 16.4.2 | Multiperiod Precautionary Saving | 244 |
| 16.5 | Illiquid Saving under Uncertainty | 246 |
| 17 | The Equilibrium Price of Time | 249 |
| 17.1 | Description of the Economy | 250 |
| 17.2 | The Determinants of the Interest Rate | 252 |
| 17.2.1 | The Interest Rate in the Absence of Growth | 252 |
| 17.2.2 | The Effect of a Sure Growth | 253 |
| 17.2.3 | The Effect of Uncertainty | 254 |
| 17.3 | The Risk-Free Rate Puzzle | 256 |
| 17.4 | The Yield Curve | 258 |
| 17.4.1 | The Pricing Formula | 258 |
| 17.4.2 | The Yield Curve with HARA Utility Functions | 260 |
| 17.4.3 | A Result When There Is No Risk of Recession | 261 |
| 17.4.4 | Exploring the Slope of the Yield Curve When There Is a Risk of Recession | 264 |
| 18 | The Liquidity Constraint | 269 |
| 18.1 | Saving as a Buffer Stock | 270 |
| 18.2 | The Liquidity Constraint Raises Risk Aversion | 272 |
| 18.3 | The Liquidity Constraint and the Shape of Absolute Risk Tolerance | 273 |
| 18.4 | Numerical Simulations | 277 |
| 19 | The Saving-Portfolio Problem | 285 |
| 19.1 | Precautionary Saving with an Endogenous Risk | 285 |
| 19.1.1 | The Case of Complete Markets | 285 |
| 19.1.2 | The Case of the Standard Portfolio Problem | 287 |
| 19.1.3 | Discussion of the Results | 288 |
| 19.2 | Optimal Portfolio Strategy with Consumption | 290 |
| 19.3 | The Merton-Samuelson Model | 291 |
| 20 | Disentangling Risk and Time | 297 |
| 20.1 | The Model of Kreps and Porteus | 298 |
| 20.2 | Preferences for an Early Resolution of Uncertainty | 299 |
| 20.3 | Prudence with Kreps-Porteus Preferences | 300 |
| VII | Equilibrium Prices of Risk and Time | 305 |
| 21 | Efficient Risk Sharing | 307 |
| 21.1 | The Case of a Static Exchange Economy | 307 |
| 21.2 | The Mutuality Principle | 309 |
| 21.3 | The Sharing of the Social Risk | 311 |
| 21.3.1 | Decomposition of the Problem | 311 |
| 21.3.2 | The Veil of Ignorance | 312 |
| 21.3.3 | Efficient Sharing Rules of the Macro Risk | 312 |
| 21.3.4 | A Two-Fund Separation Theorem | 314 |
| 21.3.5 | The Case of Small Risk per Capita | 315 |
| 21.4 | Group's Attitude toward Risk | 316 |
| 21.4.1 | The Representative Agent | 316 |
| 21.4.2 | Arrow-Lind Theorem | 317 |
| 21.4.3 | Group Decision and Individual Choice | 317 |
| 21.5 | Introducing Time and Investment | 319 |
| 21.6 | A Final Remark: The Concavity of the Certainty Equivalent Functional | 321 |
| 22 | The Equilibrium Price of Risk and Time | 327 |
| 22.1 | An Arrow-Debreu Economy | 327 |
| 22.2 | Application of the First Theorem of Welfare Economics | 328 |
| 22.3 | Pricing Arrow-Debreu Securities | 329 |
| 22.4 | Pricing by Arbitrage | 330 |
| 22.5 | The Competitive Price of Risk | 332 |
| 22.6 | The Competitive Price of Time | 334 |
| 22.7 | Spot Markets and Markets for Futures | 335 |
| 22.8 | Corporate Finance in an Arrow-Debreu Economy | 337 |
| 23 | Searching for the Representative Agent | 343 |
| 23.1 | Analytical Solution to the Aggregation Problem | 344 |
| 23.2 | Wealth Inequality, Risk Aversion, and the Equity Premium | 345 |
| 23.3 | Wealth Inequality and the Risk-Free Rate | 347 |
| 23.3.1 | The Consumption Smoothing Effect | 348 |
| 23.3.2 | The Precautionary Effect | 349 |
| VIII | Risk and Information | 355 |
| 24 | The Value of Information | 357 |
| 24.1 | The General Model of Risk and Information | 357 |
| 24.1.1 | Structure of Information | 357 |
| 24.1.2 | The Decision Problem | 358 |
| 24.1.3 | The Posterior Maximum Expected Utility Is Convex in the Vector of Posterior Probabilities | 359 |
| 24.2 | The Value of Information Is Positive | 362 |
| 24.3 | Refining the Information Structure | 364 |
| 24.3.1 | Definition and Basic Characterization | 364 |
| 24.3.2 | Garbling Messages and the Theorem of Blackwell | 366 |
| 24.3.3 | Location Experiments | 371 |
| 24.4 | The Value of Information and Risk Aversion | 373 |
| 24.4.1 | A Definition of the Value of Information | 373 |
| 24.4.2 | A Simple Illustration: The Gambler's Problem | 374 |
| 24.4.3 | The Standard Portfolio Problem | 378 |
| 25 | Decision Making and Information | 383 |
| 25.1 | A Technique for the Comparative Statics of More Informativeness | 383 |
| 25.2 | The Portfolio-Saving Problem | 386 |
| 25.3 | A Digression: Scientific Uncertainty, Global Warming, and the "Precautionary Principle" | 389 |
| 25.4 | The Saving Problem with Uncertain Returns | 390 |
| 25.5 | Precautionary Saving | 392 |
| 25.6 | The Value of Flexibility and Option Value | 393 |
| 25.7 | Predictability and Portfolio Management | 397 |
| 25.7.1 | Exogenous Predictability | 399 |
| 25.7.2 | Endogenous Predictability and Mean-Reversion | 400 |
| 26 | Information and Equilibrium | 407 |
| 26.1 | Hirshleifer Effect | 407 |
| 26.2 | Information and the Equity Premium | 413 |
| 27 | Epilogue | 423 |
| 27.1 | The Important Open Questions | 423 |
| 27.1.1 | The Independence Axiom | 423 |
| 27.1.2 | Measures of Risk Aversion | 424 |
| 27.1.3 | Qualitative Properties of the Utility Function | 425 |
| 27.1.4 | Economics of Uncertainty and Psychology | 426 |
| Bibliography | 429 | |
| Index of Lemmas and Propositions | 441 | |
| Index of Subjects | 443 |
What People are Saying About This
Gollier's treatise on risk and time will be the bible for future finance theory and practice. Get your copy; read and reread. Keep ahead of the competitive mob.
An authoritative, state-of-the art compendium on expected utility, the savings/portfolio choice problem, and much more.
Christian Gollier offers a lucid and comprehensive treatment of the theory of expected utility. He clarifies the deep structure of the theory, and systematically explores the connections between observed decisions and the preferences that generate them. This book will be an invaluable resource for students of choice under uncertainty.
—John Y. Campbell, Department of Economics, Harvard University
Christian Gollier, one of the foremost contemporary researchers on the economics of uncertainty, has written an instant classic. this path-breaking book weaves with dazzling mastery the common thread of the economics of risk and time through microeconomic theory, macroeconomics, and finance. This is a feat no one has accomplished before. This book is therefore a must read for a broad audience: graduate students in economics and finance, superior undergraduates, and researchers will all find it a source of knowledge and inspiration.
—Philippe Weil, Professor of Economics and Co-Director, European Centre for Advanced Research in Economics and Statistics, Universite Libre de BruxellesGollier's treatise on risk and time will be the bible for future finance theory and practice. Get your copy; read and reread. Keep ahead of the competitive mob.
—Paul A. Samuelson, MITChristian Gollier, one of the foremost contemporary researchers on the economics of uncertainty, has written an instant classic. this path-breaking book weaves with dazzling mastery the common thread of the economics of risk and time through microeconomic theory, macroeconomics, and finance. This is a feat no one has accomplished before. This book is therefore a must read for a broad audience: graduate students in economics and finance, superior undergraduates, and researchers will all find it a source of knowledge and inspiration.
Christian Gollier offers a lucid and comprehensive treatment of the theory of expected utility. He clarifies the deep structure of the theory, and systematically explores the connections between observed decisions and the preferences that generate them. This book will be an invaluable resource for students of choice under uncertainty.