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Optimal risk-sharing rules and equilibria with Choquet-expected-utility

Author

Listed:
  • Alain Chateauneuf

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

  • Rose Anne Dana

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

  • Jean-Marc Tallon

    () (EUREQUA - Equipe Universitaire de Recherche en Economie Quantitative - UP1 - Université 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 (as in 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 that non-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, 2000. "Optimal risk-sharing rules and equilibria with Choquet-expected-utility," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00451997, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00451997
    DOI: 10.1016/S0304-4068(00)00041-0
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00451997
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    References listed on IDEAS

    as
    1. Tallon, J.-M. & Chateauneuf, A., 1998. "Diversification, Convex Preferences and Non-Empty Core," Papiers d'Economie Mathématique et Applications 98.32, Université Panthéon-Sorbonne (Paris 1).
    2. Malinvaud, E., 1972. "The allocation of individual risks in large markets," Journal of Economic Theory, Elsevier, vol. 4(2), pages 312-328, April.
    3. Tallon, Jean-Marc, 1998. "Do sunspots matter when agents are Choquet-expected-utility maximizers?," Journal of Economic Dynamics and Control, Elsevier, vol. 22(3), pages 357-368, March.
    4. Cass, David & Chichilnisky, Graciela & Wu, Ho-Mou, 1996. "Individual Risk and Mutual Insurance," Econometrica, Econometric Society, vol. 64(2), pages 333-341, March.
    5. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    6. Malinvaud, E, 1973. "Markets for an Exchange Economy with Individual Risks," Econometrica, Econometric Society, vol. 41(3), pages 383-410, May.
    7. Dow, James & Werlang, Sergio Ribeiro da Costa, 1992. "Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio," Econometrica, Econometric Society, vol. 60(1), pages 197-204, January.
    8. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
    9. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    10. Antoine Billot & Alain Chateauneuf & Itzhak Gilboa & Jean-Marc Tallon, 2000. "Sharing Beliefs: Between Agreeing and Disagreeing," Econometrica, Econometric Society, vol. 68(3), pages 685-694, May.
    11. repec:adr:anecst:y:1997:i:48:p:10 is not listed on IDEAS
    12. Sujoy Mukerji, 1996. "Understanding the nonadditive probability decision model (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 23-46.
    13. Karni, Edi & Schmeidler, David, 1991. "Utility theory with uncertainty," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 33, pages 1763-1831, Elsevier.
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    More about this item

    Keywords

    Choquet expected utility; comonotonicity; risk-sharing; equilibrium;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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