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Updating Choquet valuation and discounting information arrivals

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  • 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. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  2. Ehud Lehrer, 2004. "Updating Non-Additive Probabilities -- A Geometric Approach," Game Theory and Information 0405010, EconWPA.
  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.
  4. Jonathan Shalev, 1994. "Loss Aversion in a Multi-Period Model," Game Theory and Information 9407001, EconWPA, revised 18 Mar 1997.
  5. Chateauneuf, Alain & Rebille, Yann, 2004. "Some characterizations of non-additive multi-period models," Mathematical Social Sciences, Elsevier, vol. 48(3), pages 235-250, November.
  6. Itzhak Gilboa & David Schmeidler, 1991. "Updating Ambiguous Beliefs," Discussion Papers 924, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Gilboa, Itzhak, 1989. "Expectation and Variation in Multi-period Decisions," Econometrica, Econometric Society, vol. 57(5), pages 1153-69, September.
  8. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
  9. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  10. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  11. Sarin, Rakesh & Wakker, Peter P, 1998. "Dynamic Choice and NonExpected Utility," Journal of Risk and Uncertainty, Springer, vol. 17(2), pages 87-119, November.
  12. Wakker, Peter, 1989. "Continuous subjective expected utility with non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 18(1), pages 1-27, February.
  13. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
  14. Jaffray, J.Y., 1992. "Dynamic Decision Making with belief Functions," Papiers d'Economie Mathématique et Applications 92.63, Université Panthéon-Sorbonne (Paris 1).
  15. Grant, Simon & Eichberger, Jürgen & Kelsey, David, 2004. "CEU Preferences and Dynamic Consistency," Sonderforschungsbereich 504 Publications 04-47, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
  16. De Waegenaere, Anja & Kast, Robert & Lapied, Andre, 2003. "Choquet pricing and equilibrium," Insurance: Mathematics and Economics, Elsevier, vol. 32(3), pages 359-370, July.
  17. De Waegenaere, Anja & Wakker, Peter P., 2001. "Nonmonotonic Choquet integrals," Journal of Mathematical Economics, Elsevier, vol. 36(1), pages 45-60, September.
  18. Schmeidler, D. & Karni, E., 1990. "A Temporal Dynamic Consistency And Expected Utility Theory," Papers 39-90, Tel Aviv.
  19. Cohen, M. & Gilboa, I. & Jaffray, J.Y. & Schmeidler, D., 2000. "An experimental study of updating ambiguous beliefs," Risk, Decision and Policy, Cambridge University Press, vol. 5(02), pages 123-133, June.
  20. 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.
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  22. 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.
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Cited by:
  1. Jurgen Eichberger & Simon Grant & David Kelsey, 2006. "Updating Choquet Beliefs," Discussion Papers 0607, Exeter University, Department of Economics.

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