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Risk aversion for variational and multiple-prior preferences

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  • Werner, Jan
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    Abstract

    The objective of this paper is to identify variational preferences and multiple-prior (maxmin) expected utility functions that exhibit aversion to risk under some probability measure from among the priors. Risk aversion has profound implications on agents’ choices and on market prices and allocations. Our approach to risk aversion relies on the theory of mean-independent risk of Werner (2009). We identify necessary and sufficient conditions for risk aversion of convex variational preferences and concave multiple-prior expected utilities. The conditions are stability of the cost function and of the set of probability priors, respectively, with respect to a probability measure. The two stability properties are new concepts. We show that cost functions defined by the relative entropy distance or other divergence distances have that property. Set of priors defined as cores of convex distortions of probability measures or neighborhoods in divergence distances have that property, too.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Mathematical Economics.

    Volume (Year): 47 (2011)
    Issue (Month): 3 ()
    Pages: 382-390

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    Handle: RePEc:eee:mateco:v:47:y:2011:i:3:p:382-390

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    Web page: http://www.elsevier.com/locate/jmateco

    Related research

    Keywords: Risk aversion; Mean-independent risk; Multiple-prior expected utility; Variational preferences;

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    References

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    1. Klaus Nehring, . "Capacities And Probabilistic Beliefs: A Precarious Coexistence," Department of Economics 97-08, California Davis - Department of Economics.
    2. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    3. H. Henry Cao & Tan Wang & Harold H. Zhang, 2005. "Model Uncertainty, Limited Market Participation, and Asset Prices," Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1219-1251.
    4. Simon Grant & Atsushi Kajii, 2005. "Probabilistically Sophisticated Multiple Priors," KIER Working Papers 608, Kyoto University, Institute of Economic Research.
    5. Massimo Marinacci, 2001. "Probabilistic sophistication and multiple priors," ICER Working Papers - Applied Mathematics Series 08-2001, ICER - International Centre for Economic Research.
    6. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    7. Strzalecki, Tomasz & Werner, Jan, 2011. "Efficient allocations under ambiguity," Journal of Economic Theory, Elsevier, vol. 146(3), pages 1173-1194, May.
    8. Tomasz Strzalecki, . "Probabilistic Sophistication and Variational Preferences," Working Paper 8337, Harvard University OpenScholar.
    9. Hong, Chew Soo & Karni, Edi & Safra, Zvi, 1987. "Risk aversion in the theory of expected utility with rank dependent probabilities," Journal of Economic Theory, Elsevier, vol. 42(2), pages 370-381, August.
    10. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
    11. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    12. Thomas J. Sargent & LarsPeter Hansen, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 60-66, May.
    13. Epstein, Larry G. & Schneider, Martin, 2003. "Recursive multiple-priors," Journal of Economic Theory, Elsevier, vol. 113(1), pages 1-31, November.
    14. LeRoy,Stephen F. & Werner,Jan, 2001. "Principles of Financial Economics," Cambridge Books, Cambridge University Press, number 9780521586054, April.
    15. Epstein Larry G. & Wang Tan, 1995. "Uncertainty, Risk-Neutral Measures and Security Price Booms and Crashes," Journal of Economic Theory, Elsevier, vol. 67(1), pages 40-82, October.
    16. Jan Werner, 2009. "Risk and risk aversion when states of nature matter," Economic Theory, Springer, vol. 41(2), pages 231-246, November.
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