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Exact capacities and star shaped distorted probabilities

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  • Zaier Aouani

    (CERMSEM)

Abstract

We are interested in this work, in capacities which are deformations of probability i.e. v = f o P, we characterize respectively balanced, totally balanced, exact and convex capacities by properties concerning the probability transformation function f. And we give the explicit expression, in the case of a convex capacity v = f o P, of a probability in the core of v which coincides with v on a given finite chain of elements of the algebra A. We end this work by two notions of increase in risk recently studied in [4] and connected with star-shaped functions and with an application to the optimality of the deductible insurance studied in [14]

Suggested Citation

  • Zaier Aouani, 2004. "Exact capacities and star shaped distorted probabilities," Cahiers de la Maison des Sciences Economiques b04117, Université Panthéon-Sorbonne (Paris 1).
    • Handle: RePEc:mse:wpsorb:b04117
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    References listed on IDEAS

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    1. Ian Jewitt, 1989. "Choosing Between Risky Prospects: The Characterization of Comparative Statics Results, and Location Independent Risk," Management Science, INFORMS, vol. 35(1), pages 60-70, January.
    2. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    3. Chateauneuf, Alain, 1991. "On the use of capacities in modeling uncertainty aversion and risk aversion," Journal of Mathematical Economics, Elsevier, vol. 20(4), pages 343-369.
    4. Gilboa, Itzhak & Lehrer, Ehud, 1991. "The value of information - An axiomatic approach," Journal of Mathematical Economics, Elsevier, vol. 20(5), pages 443-459.
    5. Jean-Marc Tallon & Alain Chateauneuf, 2002. "Diversification, convex preferences and non-empty core in the Choquet expected utility model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(3), pages 509-523.
    6. DELBAEN, Freddy, 1974. "Convex games and extreme points," LIDAM Reprints CORE 159, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Itzhak Gilboa & David Schmeidler, 1992. "Canonical Representation of Set Functions," Discussion Papers 986, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    9. Itzhak Gilboa & David Schmeidler, 1995. "Canonical Representation of Set Functions," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 197-212, February.
    10. Chateauneuf, Alain & Cohen, Michele & Meilijson, Isaac, 2004. "Four notions of mean-preserving increase in risk, risk attitudes and applications to the rank-dependent expected utility model," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 547-571, August.
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    Cited by:

    1. Felix-Benedikt Liebrich & Cosimo Munari, 2022. "Law-Invariant Functionals that Collapse to the Mean: Beyond Convexity," Mathematics and Financial Economics, Springer, volume 16, number 2, September.
    2. Max Nendel & Jan Streicher, 2023. "An axiomatic approach to default risk and model uncertainty in rating systems," Papers 2303.08217, arXiv.org, revised Sep 2023.
    3. Moez Abouda & Elyess Farhoud, 2010. "Anti-comonotone random variables and anti-monotone risk aversion," Post-Print halshs-00497444, HAL.
    4. Erio Castagnoli & Giacomo Cattelan & Fabio Maccheroni & Claudio Tebaldi & Ruodu Wang, 2021. "Star-shaped Risk Measures," Papers 2103.15790, arXiv.org, revised Apr 2022.
    5. Moez Abouda & Elyess Farhoud, 2010. "Risk aversion and Relationships in model-free," Post-Print halshs-00492170, HAL.
    6. Nendel, Max & Streicher, Jan, 2023. "An axiomatic approach to default risk and model uncertainty in rating systems," Journal of Mathematical Economics, Elsevier, vol. 109(C).

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    More about this item

    Keywords

    Cooperative game; capacity; balanced; exact; core; increase in risk;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General

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