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Diversification, convex preferences and non-empty core in the Choquet expected utility model

Author

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  • Alain Chateauneuf

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Rose Anne Dana

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Jean-Marc Tallon

    (EUREQUA - Equipe Universitaire de Recherche en Economie Quantitative - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper explores risk-sharing and equilibrium in a general equilibrium set-up wherein agents are non-additive expected utility maximizers. We show that when agents have the same convex capacity, the set of Pareto-optima is independent of it and identical to the set of optima of an economy in which agents are expected utility maximizers and have same probability. Hence, optimal allocations are comonotone. This enables us to study the equilibrium set. When agents have different capacities, matters are much more complex (asin the vNM case). We give a general characterization and show how it simplifies when Pareto-optima are comonotone. We use this result to characterize Pareto-optima when agents have capacities that are the convex transform of some probability distribution. comonotonicity of Pareto-optima is also shown to be true in the two-state case if the intersection of the core of agents' capacities is non-empty; Pareto-optima may then be fully characterized in the two-agent, two-state case. This comonotonicity result does not generalize to more than two states as we show with a counter-example. Finally, if there is no-aggregate risk, we show thatnon-empty core intersection is enough to guarantee that optimal allocations are full-insurance allocation. This result does not require convexity of preferences.

Suggested Citation

  • Alain Chateauneuf & Rose Anne Dana & Jean-Marc Tallon, 2002. "Diversification, convex preferences and non-empty core in the Choquet expected utility model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00174770, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00174770
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00174770
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    References listed on IDEAS

    as
    1. 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.
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    More about this item

    Keywords

    Choquet expected utility; comonotonicity; risk-sharing; equilibrium;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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