The Effects of Changes in Risk on Risk Taking: A Survey

We examine an important class of decision problems under uncertainty that entails the standard portfolio problem and the demand for coinsurance. The agent faces a controllable risk—his demand for a risky asset, for example—and a background risk. We determine how a change in the distribution in one of these two risks affects the optimal exposure to the controllable risk. Restrictions on first-order and second-order stochastic dominance orders are in general necessary to yield an unambiguous comparative statics property. We also review another line of research in which restrictions are made on preferences rather than on stochastic dominance orders.

[1]  LevyHaim.  Stochastic Dominance and Expected Utility , 1992 .

[2]  Robert L. Winkler,et al.  Risky Choices and Correlated Background Risk , 2005, Manag. Sci..

[3]  Josef Hadar,et al.  Rules for Ordering Uncertain Prospects , 1969 .

[4]  M. Rothschild,et al.  Increasing risk II: Its economic consequences , 1971 .

[5]  Jingyuan Li,et al.  The demand for a risky asset in the presence of a background risk , 2011, J. Econ. Theory.

[6]  A Ratio Criterion for Signing the Effects of an Increase in Uncertainty , 1989 .

[7]  Christian Gollier,et al.  Increased Risk-Bearing with Background Risk , 2006 .

[8]  Louis Eeckhoudt,et al.  Risk: Evaluation, Management and Sharing , 1996 .

[9]  John H. Lindsey,et al.  Investment Flexibility and the Acceptance of Risk , 1997 .

[10]  A Note on Portfolio Dominance , 1997 .

[11]  A. Sandmo.  On the theory of the competitive firm under price uncertainty , 1971 .

[12]  C. Gollier,et al.  A model of comparative statics for changes in stochastic returns with dependent risky assets , 1995 .

[13]  Wayne Shafer,et al.  Some Results on Comparative Statics under Uncertainty , 1987 .

[14]  Jack A. Meyer,et al.  Strong Increases in Risk and Their Comparative Statics , 1985 .

[15]  Harris Schlesinger,et al.  Multiplicative Background Risk , 2006, Manag. Sci..

[16]  Isaac Meilijson,et al.  Demand for risky financial assets: A portfolio analysis , 1990 .

[17]  L. Eeckhoudt,et al.  Minimum and Maximum Prices, Uncertainty, and the Theory of the Competitive Firm , 1980 .

[18]  Luc Arrondel,et al.  Portfolio Choice and Background Risk: Theory and Evidence. ∗ , 2003 .

[19]  Miles S. Kimball,et al.  Standard Risk Aversion , 1991 .

[20]  A Note on Optimal Insurance in the presence of a Nonpecuniary Background Risk , 2003 .

[21]  J. Pratt.  RISK AVERSION IN THE SMALL AND IN THE LARGE11This research was supported by the National Science Foundation (grant NSF-G24035). Reproduction in whole or in part is permitted for any purpose of the United States Government. , 1964 .

[22]  L. Eeckhoudt,et al.  The economics of adding and subdividing independent risks: Some comparative statics results , 1993 .

[23]  Tae Kun Seo,et al.  The Effects of Shifts in a Return Distribution on Optimal Portfolios , 1990 .

[24]  Harris Schlesinger,et al.  Optimal Insurance in Incomplete Markets , 1983, Journal of Political Economy.

[25]  G. Dionne.  Contributions to insurance economics , 1992 .

[26]  Agnar Sandmo,et al.  "Fixed Costs" and the Competitive Firm Under Price Uncertainty: Reply , 1972 .

[27]  H. Levy.  Stochastic dominance and expected utility: survey and analysis , 1992 .

[28]  Christian Gollier,et al.  The Comparative Statics of Changes in Risk Revisited , 1995 .

[29]  M. Rothschild,et al.  Increasing risk: I. A definition , 1970 .

[30]  C. Gollier,et al.  Comparative Statics Under Multiple Sources of Risk with Applications to Insurance Demand , 1992 .

[31]  Susan Athey,et al.  Comparative Statics Under Uncertainty: Single Crossing Properties and Log-Supermodularity , 1998 .

[32]  Increases in Risk and Linear Payoffs , 1993 .

[33]  C. Gollier,et al.  Portfolio choice under noisy asset returns , 1996 .

[34]  Paul R. Milgrom,et al.  Good News and Bad News: Representation Theorems and Applications , 1981 .

[35]  Edward Schlee,et al.  Comparative Statics under Uncertainty for a Class of Economic Agents , 1993 .

[36]  Christian Gollier,et al.  Risk Vulnerability and the temper-ing E ect of Background Risk , 1996 .

[37]  R. Kihlstrom,et al.  RISK AVERSION WITH RANDOM INITIAL WEALTH , 1981 .

[38]  Louis Eeckhoudt,et al.  Changes in Background Risk and Risk Taking Behavior , 1996 .

[39]  L. Eeckhoudt,et al.  Demand for risky assets and the monotone probability ratio order , 1995 .

[40]  Increases in Risk and Optimal Portfolio , 1997 .

[41]  Jack Meyer,et al.  Deterministic transformations of random variables and the comparative statics of risk , 1989 .

[42]  Christian Gollier,et al.  The Spillover Effect of Compulsory Insurance , 1994 .

[43]  Peter C. Fishburn,et al.  Optimal Portfolios with One Safe and One Risky Asset: Effects of Changes in Rate of Return and Risk , 1976 .

[44]  Louis Eeckhoudt,et al.  Increases in Risk and the Demand for Insurance , 1990 .

[45]  Donald J. Meyer,et al.  Changes in Background Risk and the Demand for Insurance , 1998 .

[46]  Louis Eeckhoudt,et al.  Background Risk, Prudence, and the Demand for Insurance , 1992 .