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The Economics of Risk and Time : The MIT Press - Christian Gollier

The Economics of Risk and Time

The MIT Press

Paperback Published: 20th August 2004
ISBN: 9780262572248
Number Of Pages: 445
For Ages: 18+ years old

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Winner, 2003 Kulp-Wright Book Award from the American Risk and Insurance Association (ARIA) and Awarded the 2001 Paul A. Samuelson Award presented by the TIAA-CREF Institute for Outstanding Scholarly Writing on Lifelong Financial Security This book updates and advances the theory of expected utility as applied to risk analysis and financial decision making. Von Neumann and Morgenstern pioneered the use of expected utility theory in the 1940s, but most utility functions used in financial management are still relatively simplistic and assume a mean-variance world. Taking into account recent advances in the economics of risk and uncertainty, this book focuses on richer applications of expected utility in finance, macroeconomics, and environmental economics. 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.

Industry Reviews

"Presents a unified and up-to-date analysis of the expected utility model and its use in determining optimal behavior under uncertainty and takes an innovative approach in choosing not to use the convenient utility functions that limit most analyses." - Journal of Economic Literature; "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." - Paul A. Samuelson, Massachusetts Institute of Technology

Prefacep. xv
Acknowledgmentsp. xix
General Theoryp. 1
The Expected Utility Modelp. 3
Simple and Compound Lotteriesp. 3
Axioms on Preferences under Uncertaintyp. 4
The Expected Utility Theoremp. 6
Critics of the Expected Utility Modelp. 9
The Allais Paradoxp. 10
The Allais Paradox and Time Consistencyp. 11
Risk Aversionp. 17
Characterization of Risk Aversionp. 17
Comparative Risk Aversionp. 18
Certainty Equivalent and Risk Premiump. 20
The Arrow-Pratt Approximationp. 21
Decreasing Absolute Risk Aversionp. 24
Some Classical Utility Functionsp. 25
Test for Your Own Degree of Risk Aversionp. 29
An Application: The Cost of Macroeconomic Risksp. 32
Change in Riskp. 39
The Extremal Approachp. 40
Second-Order Stochastic Dominancep. 42
Diversificationp. 45
First-Order Stochastic Dominancep. 46
The Standard Portfolio Problemp. 51
The Standard Portfolio Problemp. 53
The Model and Its Basic Propertiesp. 53
The Case of a Small Riskp. 55
The Case of HARA Functionsp. 57
The Impact of Risk Aversionp. 58
The Impact of a Change in Riskp. 59
The Equilibrium Price of Riskp. 65
A Simple Equilibrium Model for Financial Marketsp. 65
The Equity Premium Puzzlep. 68
The Equity Premium with Limited Participationp. 71
The Equity Premium and the Integration of International Financial Marketsp. 73
Some Technical Tools and Their Applicationsp. 79
A Hyperplane Separation Theoremp. 81
The Diffidence Theoremp. 81
Link with the Jensen's Inequalityp. 88
Applications of the Diffidence Theoremp. 89
Diffidencep. 89
Comparative Diffidencep. 90
Central Risk Aversionp. 91
Central Riskinessp. 92
The Covariance Rulep. 94
Log-Supermodularityp. 99
Definitionp. 99
Log-Supermodularity and Single Crossingp. 102
A Theoretical Resultp. 102
Applications to the Standard Portfolio Problemp. 103
Jewitt's Preference Ordersp. 104
Expectation of a Log-Supermodular Functionp. 105
A Theoretical Resultp. 105
Two Applicationsp. 106
Multiple Risksp. 111
Risk Aversion with Background Riskp. 113
Preservation of DARAp. 114
The Comparative Risk Aversion Is Not Preservedp. 117
Extensions with Dependent Background Riskp. 119
Affiliated Background Riskp. 119
The Comparative Risk Aversion in the Sense of Rossp. 121
The Tempering Effect of Background Riskp. 125
Risk Vulnerabilityp. 126
Risk Vulnerability and Increase in Riskp. 130
Increase in Background Riskp. 130
Increase in the Endogenous Riskp. 130
Risk Vulnerability and the Equity Premium Puzzlep. 131
Generalized Risk Vulnerabilityp. 132
Standardnessp. 135
Taking Multiple Risksp. 141
The Interaction between Asset Demand and Small Gamblesp. 142
Are Independent Assets Substitutes?p. 144
The i.i.d. Casep. 144
The General Casep. 150
The Dynamic Investment Problemp. 155
Static versus Dynamic Optimizationp. 157
The Standard Portfolio Problemp. 158
The Modelp. 158
The HARA Casep. 160
A Sufficient Condition for Younger People to Be More Risk-Aversep. 161
Discussion of the Resultsp. 165
Nonlinear Risk Tolerancep. 165
Nondifferentiable Marginal Utilityp. 166
Background Risk and Time Horizonp. 168
Investors Bear a Background Risk at Retirementp. 168
Stationary Income Processp. 171
Special Topics in Dynamic Financep. 175
The Length of Periods between Tradep. 175
Dynamic Discrete Choicep. 179
Constraints on Feasible Strategiesp. 183
The Effect of a Leverage Constraintp. 185
The Case of a Lower Bound on the Investment in the Risky Assetp. 185
The Case of an Upper Bound on the Investment in the Risky Assetp. 187
The Arrow-Debreu Portfolio Problemp. 193
The Demand for Contingent Claimsp. 195
The Modelp. 196
Characterization of the Optimal Portfoliop. 197
The Impact of Risk Aversionp. 200
Risk on Wealthp. 205
The Marginal Propensity to Consume in State [pi]p. 206
The Preservation of DARA and IARAp. 208
The Marginal Value of Wealthp. 210
Aversion to Risk on Wealthp. 211
Consumption and Savingp. 215
Consumption under Certaintyp. 217
Time Separabilityp. 217
Exponential Discountingp. 218
Consumption Smoothing under Certaintyp. 219
Analogy with the Portfolio Problemp. 221
The Social Cost of Volatilityp. 224
The Marginal Propensity to Consumep. 226
Time Diversification and Self-Insurancep. 227
Precautionary Saving and Prudencep. 235
Prudencep. 235
The Demand for Savingp. 239
The Marginal Propensity to Consume under Uncertaintyp. 239
Does Uncertainty Increase the MPC?p. 240
Does Uncertainty Make the MPC Decreasing in Wealth?p. 241
More Than Two Periodsp. 242
The Euler Equationp. 242
Multiperiod Precautionary Savingp. 244
Illiquid Saving under Uncertaintyp. 246
The Equilibrium Price of Timep. 249
Description of the Economyp. 250
The Determinants of the Interest Ratep. 252
The Interest Rate in the Absence of Growthp. 252
The Effect of a Sure Growthp. 253
The Effect of Uncertaintyp. 254
The Risk-Free Rate Puzzlep. 256
The Yield Curvep. 258
The Pricing Formulap. 258
The Yield Curve with HARA Utility Functionsp. 260
A Result When There Is No Risk of Recessionp. 261
Exploring the Slope of the Yield Curve When There Is a Risk of Recessionp. 264
The Liquidity Constraintp. 269
Saving as a Buffer Stockp. 270
The Liquidity Constraint Raises Risk Aversionp. 272
The Liquidity Constraint and the Shape of Absolute Risk Tolerancep. 273
Numerical Simulationsp. 277
The Saving-Portfolio Problemp. 285
Precautionary Saving with an Endogenous Riskp. 285
The Case of Complete Marketsp. 285
The Case of the Standard Portfolio Problemp. 287
Discussion of the Resultsp. 288
Optimal Portfolio Strategy with Consumptionp. 290
The Merton-Samuelson Modelp. 291
Disentangling Risk and Timep. 297
The Model of Kreps and Porteusp. 298
Preferences for an Early Resolution of Uncertaintyp. 299
Prudence with Kreps-Porteus Preferencesp. 300
Equilibrium Prices of Risk and Timep. 305
Efficient Risk Sharingp. 307
The Case of a Static Exchange Economyp. 307
The Mutuality Principlep. 309
The Sharing of the Social Riskp. 311
Decomposition of the Problemp. 311
The Veil of Ignorancep. 312
Efficient Sharing Rules of the Macro Riskp. 312
A Two-Fund Separation Theoremp. 314
The Case of Small Risk per Capitap. 315
Group's Attitude toward Riskp. 316
The Representative Agentp. 316
Arrow-Lind Theoremp. 317
Group Decision and Individual Choicep. 317
Introducing Time and Investmentp. 319
A Final Remark: The Concavity of the Certainty Equivalent Functionalp. 321
The Equilibrium Price of Risk and Timep. 327
An Arrow-Debreu Economyp. 327
Application of the First Theorem of Welfare Economicsp. 328
Pricing Arrow-Debreu Securitiesp. 329
Pricing by Arbitragep. 330
The Competitive Price of Riskp. 332
The Competitive Price of Timep. 334
Spot Markets and Markets for Futuresp. 335
Corporate Finance in an Arrow-Debreu Economyp. 337
Searching for the Representative Agentp. 343
Analytical Solution to the Aggregation Problemp. 344
Wealth Inequality, Risk Aversion, and the Equity Premiump. 345
Wealth Inequality and the Risk-Free Ratep. 347
The Consumption Smoothing Effectp. 348
The Precautionary Effectp. 349
Risk and Informationp. 355
The Value of Informationp. 357
The General Model of Risk and Informationp. 357
Structure of Informationp. 357
The Decision Problemp. 358
The Posterior Maximum Expected Utility Is Convex in the Vector of Posterior Probabilitiesp. 359
The Value of Information Is Positivep. 362
Refining the Information Structurep. 364
Definition and Basic Characterizationp. 364
Garbling Messages and the Theorem of Blackwellp. 366
Location Experimentsp. 371
The Value of Information and Risk Aversionp. 373
A Definition of the Value of Informationp. 373
A Simple Illustration: The Gambler's Problemp. 374
The Standard Portfolio Problemp. 378
Decision Making and Informationp. 383
A Technique for the Comparative Statics of More Informativenessp. 383
The Portfolio-Saving Problemp. 386
A Digression: Scientific Uncertainty, Global Warming, and the "Precautionary Principle"p. 389
The Saving Problem with Uncertain Returnsp. 390
Precautionary Savingp. 392
The Value of Flexibility and Option Valuep. 393
Predictability and Portfolio Managementp. 397
Exogenous Predictabilityp. 399
Endogenous Predictability and Mean-Reversionp. 400
Information and Equilibriump. 407
Hirshleifer Effectp. 407
Information and the Equity Premiump. 413
Epiloguep. 423
The Important Open Questionsp. 423
The Independence Axiomp. 423
Measures of Risk Aversionp. 424
Qualitative Properties of the Utility Functionp. 425
Economics of Uncertainty and Psychologyp. 426
Bibliographyp. 429
Index of Lemmas and Propositionsp. 441
Index of Subjectsp. 443
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780262572248
ISBN-10: 0262572249
Series: The MIT Press
Audience: Professional
For Ages: 18+ years old
Format: Paperback
Language: English
Number Of Pages: 445
Published: 20th August 2004
Publisher: MIT Press Ltd
Country of Publication: US
Dimensions (cm): 22.23 x 14.61  x 1.27
Weight (kg): 0.58