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Ambiguity through confidence functions

  • Chateauneuf, Alain
  • Faro, José Heleno

We characterize preference relations over bounded below Anscombe and Aumann's acts and give necessary and sufficient conditions that guarantee the existence of a utility function u on consequences, a confidence function [phi] on the set of all probabilities over states of nature, and a positive threshold level of confidence [alpha]0 such that our preference relation has a functional representation J, where given an act f The level set L[alpha]0[phi]:={p:[phi](p)>=[alpha]0} reflects the priors held by the decision maker and the value [phi](p) captures the relevance of prior p for his decision. The combination of [phi] and [alpha]0 may describe the decision maker's subjective assessment of available information. An important feature of our representation is the characterization of the maximal confidence function which allows us to obtain results on comparative ambiguity aversion and on special cases, namely the subjective expected utility, the Choquet expected utility with convex capacity, and the maxmin expected utility.

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

Volume (Year): 45 (2009)
Issue (Month): 9-10 (September)
Pages: 535-558

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Handle: RePEc:eee:mateco:v:45:y:2009:i:9-10:p:535-558
Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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  1. Sujoy Mukerji & Peter Klibanoff, 2002. "A Smooth Model of Decision,Making Under Ambiguity," Economics Series Working Papers 113, University of Oxford, Department of Economics.
  2. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci, 2002. "Certainty Independence and the Separation of Utility and Beliefs," ICER Working Papers - Applied Mathematics Series 40-2002, ICER - International Centre for Economic Research.
  3. Chateauneuf, Alain, 1991. "On the use of capacities in modeling uncertainty aversion and risk aversion," Journal of Mathematical Economics, Elsevier, vol. 20(4), pages 343-369.
  4. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2004. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Carlo Alberto Notebooks 12, Collegio Carlo Alberto, revised 2006.
  5. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2001. "A subjective spin on roulette wheels," ICER Working Papers - Applied Mathematics Series 17-2001, ICER - International Centre for Economic Research, revised Aug 2001.
  6. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
  7. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
  8. Thomas J. Sargent & LarsPeter Hansen, 2001. "Robust Control and Model Uncertainty," American Economic Review, American Economic Association, vol. 91(2), pages 60-66, May.
  9. F J Anscombe & R J Aumann, 2000. "A Definition of Subjective Probability," Levine's Working Paper Archive 7591, David K. Levine.
  10. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
  11. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  12. 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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