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Coping with Imprecise Information : A Decision Theoretic Approach

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  • Thibault Gadjos

    (Crest)

  • Jean-Marc Tallon

    (Crest)

  • Jean-Christophe Vergnaud

    (Crest)

Abstract

We provide a model of decision making under uncertainty in which the decision maker reacts toimprecision of the available data. Data is represented by a set of probability distributions. Weaxiomatize a decision criterion of the maxmin expected utility type, in which the revealed setof priors explicitly depends on the available data. We then characterize notions of comparativeaversion 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 utilityfunction, which embeds risk attitudes. We also give a more specific result, in which the functionalrepresenting the decision maker’s preferences is the convex combination of the minimumexpected utility with respect to the available data and expected utility with respect to a subjectiveprobability distribution, interpreted as a reference prior. This particular form is shown tobe equivalent to some form of constant aversion to imprecision. We finally provide examples ofapplications first to unanimity rankings of imprecision and risk and then to optimal risk sharingarrangements.

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Bibliographic Info

Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2004-14.

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Date of creation: 2004
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Handle: RePEc:crs:wpaper:2004-14

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  1. repec:hal:cesptp:halshs-00174539 is not listed on IDEAS
  2. 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.
  3. 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.
  4. Wojciech Olszewski, 2007. "Preferences Over Sets of Lotteries -super-1," Review of Economic Studies, Oxford University Press, vol. 74(2), pages 567-595.
  5. Sujoy Mukerji & Jean-Marc Tallon, 2000. "Ambiguity Aversion and Incompleteness of Financial Markets," Economics Series Working Papers 46, University of Oxford, Department of Economics.
  6. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
  7. Epstein, Larry G, 1999. "A Definition of Uncertainty Aversion," Review of Economic Studies, Wiley Blackwell, vol. 66(3), pages 579-608, July.
  8. 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.
  9. Scarsini, Marco, 1992. "Dominance conditions in non-additive expected utility theory," Journal of Mathematical Economics, Elsevier, vol. 21(2), pages 173-184.
  10. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  11. repec:hal:journl:halshs-00086021 is not listed on IDEAS
  12. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  13. 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. Thibault Gajdos & Feriel Kandil, 2008. "The ignorant observer," Social Choice and Welfare, Springer, vol. 31(2), pages 193-232, August.
  2. Marciano Siniscalchi, 2007. "Vector Expected Utility and Attitudes toward Variation," Discussion Papers 1455, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. repec:hal:journl:halshs-00115722 is not listed on IDEAS
  4. Henry, Marc, 2007. "A representation of decision by analogy," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 771-794, September.

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