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Risk aversion for variational and multiple-prior preferences

  • Werner, Jan

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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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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  1. Strzalecki, Tomasz, 2011. "Probabilistic Sophistication and Variational Preferences," Scholarly Articles 11352635, Harvard University Department of Economics.
  2. 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.
  3. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  4. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  5. Tomasz Strzalecki & Jan Werner, . "Efficient Allocations under Ambiguity," Working Paper 8325, Harvard University OpenScholar.
  6. Nehring, Klaus, 1999. "Capacities and probabilistic beliefs: a precarious coexistence," Mathematical Social Sciences, Elsevier, vol. 38(2), pages 197-213, September.
  7. 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.
  8. 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.
  9. 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.
  10. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  11. Simon Grant & Atsushi Kajii, 2005. "Probabilistically Sophisticated Multiple Priors," KIER Working Papers 608, Kyoto University, Institute of Economic Research.
  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. Larry G. Epstein & Martin Schneider, 2001. "Recursive Multiple-Priors," RCER Working Papers 485, University of Rochester - Center for Economic Research (RCER).
  14. Massimo Marinacci, 2002. "Probabilistic Sophistication and Multiple Priors," Econometrica, Econometric Society, vol. 70(2), pages 755-764, March.
  15. repec:cup:cbooks:9780521586054 is not listed on IDEAS
  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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