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Variational representation of preferences under ambiguity

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Author Info

  • Fabio Maccheroni
  • Massimo Marinacci
  • Aldo Rustichini

Abstract

In the classic Anscombe and Aumann decision setting, we give necessary and sufficient conditions that guarantee the existence of a utility function u on outcomes and an ambiguity index c on the set of all probabilities on the states of the world such that acts are ranked according to the criterion V(f)=min{E(u(f),p)+c(p)} where p ranges over all probability distributions and c is a non-negative convex funcion on the set of all probability distributions. The preferences we characterize include as special cases the multiple priors preferences of Gilboa and Schmeidler, the multiplier preferences of Hansen and Sargent, and the mean-variance preferences of Markowitz and Tobin. In this way we are able to provide a rigorous ambiguity perspective on the latter two models, which have been widely used in macroeconomics and finance.

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Bibliographic Info

Paper provided by ICER - International Centre for Economic Research in its series ICER Working Papers - Applied Mathematics Series with number 05-2004.

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Length: 55 pages
Date of creation: Mar 2004
Date of revision:
Handle: RePEc:icr:wpmath:05-2004

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References

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  1. Alain Chateauneuf & Fabio Maccheroni & Massimo Marinacci & Jean-Marc Tallon, 2005. "Monotone continuous multiple priors," Economic Theory, Springer, vol. 26(4), pages 973-982, November.
  2. Thomas J. Sargent & LarsPeter Hansen, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 60-66, May.
  3. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  4. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  5. Epstein, Larry G, 1999. "A Definition of Uncertainty Aversion," Review of Economic Studies, Wiley Blackwell, vol. 66(3), pages 579-608, July.
  6. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
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Cited by:
  1. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "Contributions to the understanding of Bayesian consistency," ICER Working Papers - Applied Mathematics Series 13-2004, ICER - International Centre for Economic Research.
  2. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On rates of convergence for posterior distributions in infinite–dimensional models," ICER Working Papers - Applied Mathematics Series 24-2004, ICER - International Centre for Economic Research.
  3. Antonio Lijoi & Igor Prünster & Stephen G. Walker, 2004. "On consistency of nonparametric normal mixtures for Bayesian density estimation," ICER Working Papers - Applied Mathematics Series 23-2004, ICER - International Centre for Economic Research.

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