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

  • Alain Chateauneuf

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - CNRS : UMR8095 - Université Paris I - Panthéon-Sorbonne)

  • Rose Anne Dana

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - CNRS : UMR7534 - Université Paris IX - Paris Dauphine)

  • Jean-Marc Tallon

    ()

    (EUREQUA - Equipe Universitaire de Recherche en Economie Quantitative - CNRS : UMR8594 - Université Paris I - Panthéon-Sorbonne)

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.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00451997.

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Date of creation: 2000
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Publication status: Published, Journal of Mathematical Economics, 2000, 34, 2, 191-214
Handle: RePEc:hal:cesptp:halshs-00451997
Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00451997
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  1. 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.
  2. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
  3. Malinvaud, E., 1972. "The allocation of individual risks in large markets," Journal of Economic Theory, Elsevier, vol. 4(2), pages 312-328, April.
  4. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  5. Billot, A. & Chateauneuf, A. & Gilboa, I. & Tallon, J.-M., 1998. "Sharing Beliefs: Between Agreeing and Disagreeing," Papiers d'Economie Mathématique et Applications 98.30, Université Panthéon-Sorbonne (Paris 1).
  6. Jean-Marc TALLON, 1997. "Risque microéconomique, aversion à l'incertitude et indétermination de l'équilibre," Annales d'Economie et de Statistique, ENSAE, issue 48, pages 211-226.
  7. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  8. Mukerji, S., 1995. "Understanding the nonadditive probability decision model," Discussion Paper Series In Economics And Econometrics 9517, Economics Division, School of Social Sciences, University of Southampton.
  9. 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.
  10. 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.
  11. Malinvaud, E, 1973. "Markets for an Exchange Economy with Individual Risks," Econometrica, Econometric Society, vol. 41(3), pages 383-410, May.
  12. Alain Chateauneuf & Jean-Marc Tallon, 2000. "Diversification, Convex Preferences and Non-Empty Core," Econometric Society World Congress 2000 Contributed Papers 0751, Econometric Society.
  13. Cass, David & Chichilnisky, Graciela & Wu, Ho-Mou, 1996. "Individual Risk and Mutual Insurance," Econometrica, Econometric Society, vol. 64(2), pages 333-41, March.
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