Risk Aversion with State-Dependent Preferences in the Rank-Dependent Expected Utility Theory

W. Henry Chiu
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W. Henry Chiu: School of Economic Studies, The University of Manchester, M13 9PL Manchester, England

The Geneva Risk and Insurance Review, 1996, vol. 21, issue 2, 159-177

Abstract: We extend the analysis of risk aversion with state-dependent preferences to the rank-dependent expected utility theory. We find that in this extended theory, for two preference relations to be comparable in risk aversion not only do their reference sets need to coincide (a condition first introduced by Karni [1983, 1985] in the original expected utility framework), but they must also rank the prospective state-dependent outcomes in the same manner. We formalize this additional condition by introducing the concept of certainty sets. Under our condition of comparability, various results and characterizations of interpersonal comparison of risk aversion are obtained. The implications for a specific insurance problem are also discussed. The Geneva Papers on Risk and Insurance Theory (1996) 21, 159–177. doi:10.1007/BF00941936

Date: 1996
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