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Coping with imprecise information : a decision theoretic approach

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  • Thibault Gajdos

    ()
    (CREST)

  • Jean-Marc Tallon

    ()
    (EUREQua)

  • Jean-Christophe Vergnaud

    ()
    (EUREQua)

Abstract

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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File URL: ftp://mse.univ-paris1.fr/pub/mse/cahiers2004/V04056.pdf
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Bibliographic Info

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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Keywords: Imprecision; ambiguity; uncertainty; decision; multiple priors.;

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References

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  1. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  2. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  3. 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.
  4. Thibault Gajdos & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2002. "Decision Making with Imprecise Probabilistic Information," ICER Working Papers - Applied Mathematics Series 18-2003, ICER - International Centre for Economic Research, revised May 2003.
  5. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  6. Epstein, Larry G, 1999. "A Definition of Uncertainty Aversion," Review of Economic Studies, Wiley Blackwell, vol. 66(3), pages 579-608, July.
  7. Scarsini, Marco, 1992. "Dominance conditions in non-additive expected utility theory," Journal of Mathematical Economics, Elsevier, vol. 21(2), pages 173-184.
  8. Sujoy Mukerji & Peter Klibanoff, 2002. "A Smooth Model of Decision,Making Under Ambiguity," Economics Series Working Papers 113, University of Oxford, Department of Economics.
  9. Mukerji, S. & Tallon, J.-M., 1999. "Ambiguity Aversion and Incompleteness of Financial Markets," Papiers d'Economie Mathématique et Applications 1999-28, Université Panthéon-Sorbonne (Paris 1).
  10. Wojciech Olszewski, 2007. "Preferences Over Sets of Lotteries -super-1," Review of Economic Studies, Oxford University Press, vol. 74(2), pages 567-595.
  11. repec:hal:journl:halshs-00086021 is not listed on IDEAS
  12. Tapking, Jens, 2004. "Axioms for preferences revealing subjective uncertainty and uncertainty aversion," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 771-797, November.
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Cited by:
  1. Marciano Siniscalchi, 2009. "Vector Expected Utility and Attitudes Toward Variation," Econometrica, Econometric Society, vol. 77(3), pages 801-855, 05.
  2. Henry, Marc, 2007. "A representation of decision by analogy," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 771-794, September.
  3. Thibault Gajdos & Feriel Kandil, 2006. "The Ignorant Observer," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00115722, HAL.
  4. repec:hal:journl:halshs-00115722 is not listed on IDEAS

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