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Smooth nonexpected utility without state independence

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  • Hengjie Ai

Abstract

We propose a notion of smoothness of nonexpected utility functions, which extends the variational analysis of nonexpected utility functions to more general settings. In particular, our theory applies to state dependent utilities, as well as the multiple prior expected utility model, both of which are not possible in previous literatures. Other nonexpected utility models are shown to satisfy smoothness under more general conditions than the Fréchet and Gateaux differentiability used in the literature. We give more general characterizations of monotonicity and risk aversion without assuming state independence of utility function.

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Paper provided by Federal Reserve Bank of Minneapolis in its series Working Papers with number 637.

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Date of creation: 2005
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Handle: RePEc:fip:fedmwp:637

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  1. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  2. Carlier, Guillaume & Dana, Rose-Anne, 2003. "Core of convex distortions of a probability," Economics Papers from University Paris Dauphine 123456789/5446, Paris Dauphine University.
  3. 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.
  4. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  5. Mark J Machina, 1982. ""Expected Utility" Analysis without the Independence Axiom," Levine's Working Paper Archive 7650, David K. Levine.
  6. Allen, Beth, 1987. "Smooth preferences and the approximate expected utility hypothesis," Journal of Economic Theory, Elsevier, vol. 41(2), pages 340-355, April.
  7. Dekel, Eddie, 1986. "An axiomatic characterization of preferences under uncertainty: Weakening the independence axiom," Journal of Economic Theory, Elsevier, vol. 40(2), pages 304-318, December.
  8. Quiggin, J. & Wakker, P., 1992. "The Axiomatic Basis of Anticipated Utility: A Clarification," Papers 9203, Tilburg - Center for Economic Research.
  9. Chew, Soo Hong, 1983. "A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox," Econometrica, Econometric Society, vol. 51(4), pages 1065-92, July.
  10. Carlier, G. & Dana, R. A., 2003. "Core of convex distortions of a probability," Journal of Economic Theory, Elsevier, vol. 113(2), pages 199-222, December.
  11. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
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Cited by:
  1. Polkovnichenko, Valery & Zhao, Feng, 2013. "Probability weighting functions implied in options prices," Journal of Financial Economics, Elsevier, vol. 107(3), pages 580-609.

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