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Updating Choquet valuation and discounting information arrivals

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Author Info

  • André Lapied

    ()
    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales (EHESS) - CNRS : UMR6579)

  • Robert Kast

    ()
    (LAMETA - Laboratoire Montpellierain d'économie théorique et appliquée - CNRS : UMR5474 - INRA : UR1135 - CIHEAM - Université Montpellier I - Montpellier SupAgro)

Abstract

We explore different possible definitions for conditional Choquet integrals and their implications for updating capacities. Many recent works consider relaxing dynamic consistency within Choquet Expected Utility models, but all of them deal with models where time is not explicitly introduced. We confront the different definitions with dynamic consistency when information arrives along with time through a Choquet version of the Net Present Value. We show that only one definition is dynamically consistent in a decision model where time is discounted according to the agent's preferences. However, it violates consequentialism because all future outcomes must be taken into consideration.

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Bibliographic Info

Paper provided by HAL in its series Working Papers with number halshs-00410532.

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Date of creation: 21 Aug 2009
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Handle: RePEc:hal:wpaper:halshs-00410532

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Related research

Keywords: Conditional Expectations; Updating; Choquet Expected Utility; Learning; Dynamic Consistency; Discounting;

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References

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  1. Jaffray, J.Y., 1992. "Dynamic Decision Making with belief Functions," Papiers d'Economie Mathématique et Applications 92.63, Université Panthéon-Sorbonne (Paris 1).
  2. De Waegenaere, Anja & Wakker, Peter P., 2001. "Nonmonotonic Choquet integrals," Journal of Mathematical Economics, Elsevier, vol. 36(1), pages 45-60, September.
  3. Alain Chateauneuf & Robert Kast & André Lapied, 2001. "Conditioning Capacities and Choquet Integrals: The Role of Comonotony," Theory and Decision, Springer, vol. 51(2), pages 367-386, December.
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  8. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
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  10. Ehud Lehrer, 2004. "Updating Non-Additive Probabilities -- A Geometric Approach," Game Theory and Information 0405010, EconWPA.
  11. Epstein Larry G. & Le Breton Michel, 1993. "Dynamically Consistent Beliefs Must Be Bayesian," Journal of Economic Theory, Elsevier, vol. 61(1), pages 1-22, October.
  12. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
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  15. De Waegenaere, Anja & Kast, Robert & Lapied, Andre, 2003. "Choquet pricing and equilibrium," Insurance: Mathematics and Economics, Elsevier, vol. 32(3), pages 359-370, July.
  16. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
  17. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  18. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-68, December.
  19. Chateauneuf, Alain & Rebille, Yann, 2004. "Some characterizations of non-additive multi-period models," Mathematical Social Sciences, Elsevier, vol. 48(3), pages 235-250, November.
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Cited by:
  1. Eichberger, Jurgen & Grant, Simon & Kelsey, David, 2007. "Updating Choquet beliefs," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 888-899, September.

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