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Conditioning Capacities and Choquet Integrals: The Role of Comonotony

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  • Alain Chateauneuf
  • Robert Kast
  • André Lapied
Abstract
Choquet integrals and capacities play a crucial role in modern decision theory. Comonotony is a central concept for these theories because the main property of a Choquet integral is its additivity for comonotone functions. We consider a Choquet integral representation of preferences showing uncertainty aversion (pessimism) and propose axioms on time consistency which yield a candidate for conditional Choquet integrals. An other axiom characterizes the role of comonotony in the use of information. We obtain two conditioning rules for capacities which amount to the well-known Bayes' and Dempster–Schafer's updating rules. We are allowed to interpret both of them as a lack of confidence in information in a dynamic extension of pessimism. Copyright Kluwer Academic Publishers 2001

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  • 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.
    • Handle: RePEc:kap:theord:v:51:y:2001:i:2:p:367-386
    DOI: 10.1023/A:1015567329595
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    References listed on IDEAS

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    1. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    2. 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(2), pages 123-133, June.
    3. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    4. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    5. Kast, R. & Lapied, A., 1997. "A Decision Theoretic Approach to Bid-Ask Spreads," G.R.E.Q.A.M. 97a17, Universite Aix-Marseille III.
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    Cited by:

    1. Robert Kast & André Lapied & Pascal Toquebeuf, 2008. "Updating Choquet Integrals , Consequentialism and Dynamic Consistency," ICER Working Papers - Applied Mathematics Series 04-2008, ICER - International Centre for Economic Research.
    2. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2009. "A characterization of the 2-additive Choquet integral through cardinal information," Post-Print halshs-00445132, HAL.
    3. Robert Kast & André Lapied & Pascal Toquebeuf, 2012. "Updating Choquet capacities: a general framework," Post-Print hal-04476906, HAL.
    4. André Lapied & Robert Kast, 2005. "Updating Choquet valuation and discounting information arrivals," Working Papers 05-09, LAMETA, Universtiy of Montpellier, revised Jan 2005.
    5. Robert Kast & André Lapied, 2010. "Valuing future cash flows with non separable discount factors and non additive subjective measures: conditional Choquet capacities on time and on uncertainty," Theory and Decision, Springer, vol. 69(1), pages 27-53, July.
    6. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2011. "A representation of preferences by the Choquet integral with respect to a 2-additive capacity," Theory and Decision, Springer, vol. 71(3), pages 297-324, September.
    7. Driouchi, Tarik & So, Raymond H.Y. & Trigeorgis, Lenos, 2020. "Investor ambiguity, systemic banking risk and economic activity: The case of too-big-to-fail," Journal of Corporate Finance, Elsevier, vol. 62(C).
    8. Rossella Agliardi, 2017. "Asymmetric Choquet random walks and ambiguity aversion or seeking," Theory and Decision, Springer, vol. 83(4), pages 591-602, December.
    9. André Lapied & Pascal Toquebeuf, 2011. "Dynamically consistent CEU preferences," Working Papers halshs-00856193, HAL.
    10. Nicolas Aubert & Bernard Grand & André Lapied & Patrick Rousseau, 2009. "Is employee ownership so senseless," Finance, Presses universitaires de Grenoble, vol. 30(2), pages 5-29.
    11. André Lapied & Thomas Rongiconi, 2013. "Ambiguity as a Source of Temptation: Modeling Unstable Beliefs," AMSE Working Papers 1316, Aix-Marseille School of Economics, France.
    12. Robert Kast & André Lapied, 2007. "Dynamically Consistent Conditional Choquet Capacities," ICER Working Papers - Applied Mathematics Series 20-2007, ICER - International Centre for Economic Research.
    13. Giulianella Coletti & Davide Petturiti & Barbara Vantaggi, 2019. "Dutch book rationality conditions for conditional preferences under ambiguity," Annals of Operations Research, Springer, vol. 279(1), pages 115-150, August.
    14. André Lapied & Pascal Toquebeuf, 2013. "A note on “Re-examining the law of iterated expectations for Choquet decision makers”," Theory and Decision, Springer, vol. 74(3), pages 439-445, March.
    15. Lapied, André & Toquebeuf, Pascal, 2012. "Dynamically consistent CEU preferences on f-convex events," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 252-256.
    16. Takashi Ui & Atsushi Kajii, 2005. "Equivalence of the Dempster-Shafer rule and the maximum likelihood rule implies convexity," Economics Bulletin, AccessEcon, vol. 4(10), pages 1-6.
    17. André Lapied & Pascal Tocquebeuf, 2007. "Consistent Dynamice Choice And Non-Expected Utility Preferences," Working Papers halshs-00353880, HAL.
    18. Robert Kast & André Lapied & Pascal Toquebeuf, 2012. "Updating Choquet capacities: a general framework," Economics Bulletin, AccessEcon, vol. 32(2), pages 1495-1503.
    19. Tarik Driouchi & Lenos Trigeorgis & Raymond H. Y. So, 2018. "Option implied ambiguity and its information content: Evidence from the subprime crisis," Annals of Operations Research, Springer, vol. 262(2), pages 463-491, March.
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