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Coping with imprecise information : a decision theoretic approach

  • Thibault Gajdos



  • Jean-Marc Tallon



  • Jean-Christophe Vergnaud



We provide a model of decision making under uncertainty in which the decision maker reacts to imprecision of the available data. Data is represented by a set of probability distributions. We axiomatize a decision criterion of the maxmin expected utility type, in which the revealed set of priors explicitly depends on the available data. We then characterize notions of comparative aversion to imprecision of the data as well as traditional notions of risk aversion. Interestingly, the study of comparative aversion to imprecision can be done independently of the utility function, which embeds risk attitudes. We also give a more specific result, in which the functional representing the decision maker's preferences is the convex combination of the minimum expected utility with respect to the available data and expected utility with respect to a subjective probability distribution, interpreted as a reference prior. This particular form is shown to be equivalent to some form of constant aversion to imprecision. We finally provide examples of applications first to unanimity rankings of imprecision and risk and then to optimal risk sharing arrangements.

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Paper provided by Université Panthéon-Sorbonne (Paris 1) in its series Cahiers de la Maison des Sciences Economiques with number v04056.

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Length: 41 pages
Date of creation: Jun 2002
Date of revision: May 2004
Handle: RePEc:mse:wpsorb:v04056
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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. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  3. Mukerji, Sujoy & Tallon, Jean-Marc, 2001. "Ambiguity Aversion and Incompleteness of Financial Markets," Review of Economic Studies, Wiley Blackwell, vol. 68(4), pages 883-904, October.
  4. repec:hal:journl:halshs-00086021 is not listed on IDEAS
  5. Thibault Gajdos & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2004. "Decision Making with Imprecise Probabilistic Information," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00086021, HAL.
  6. Tapking, Jens, 2004. "Axioms for preferences revealing subjective uncertainty and uncertainty aversion," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 771-797, November.
  7. Scarsini, Marco, 1992. "Dominance conditions in non-additive expected utility theory," Journal of Mathematical Economics, Elsevier, vol. 21(2), pages 173-184.
  8. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
  9. Wojciech Olszewski, 2007. "Preferences Over Sets of Lotteries -super-1," Review of Economic Studies, Oxford University Press, vol. 74(2), pages 567-595.
  10. Yaari, Menahem E., 1969. "Some remarks on measures of risk aversion and on their uses," Journal of Economic Theory, Elsevier, vol. 1(3), pages 315-329, October.
  11. Epstein, Larry G, 1999. "A Definition of Uncertainty Aversion," Review of Economic Studies, Wiley Blackwell, vol. 66(3), pages 579-608, July.
  12. 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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