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

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  • Tallon, Jean-Marc
  • Dana, Rose-Anne
  • Chateauneuf, Alain

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 the same probability. Hence, optimal allocations are comonotone. This enables us to study the equilibrium set. When agents have different capacities, the 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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Bibliographic Info

Paper provided by Paris Dauphine University in its series Economics Papers from University Paris Dauphine with number 123456789/5461.

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Date of creation: 2000
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Publication status: Published in Journal of Mathematical Economics, 2000, Vol. 34, no. 2. pp. 191-214.Length: 23 pages
Handle: RePEc:dau:papers:123456789/5461

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Keywords: Equilibrium; Risk-sharing; Comonotonicity; Choquet expected utility;

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  1. Tallon, J.-M. & Chateauneuf, A., 1998. "Diversification, Convex Preferences and Non-Empty Core," Papiers d'Economie Mathématique et Applications, Université Panthéon-Sorbonne (Paris 1) 98.32, Université Panthéon-Sorbonne (Paris 1).
  2. Cass, David & Chichilnisky, Graciela & Wu, Ho-Mou, 1996. "Individual Risk and Mutual Insurance," Econometrica, Econometric Society, Econometric Society, vol. 64(2), pages 333-41, March.
  3. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, Econometric Society, vol. 57(3), pages 571-87, May.
  4. Tallon, J.M., 1996. "Risque microeconomique, aversion a l'incertitude et indermination de l'equilibre," Papiers d'Economie Mathématique et Applications, Université Panthéon-Sorbonne (Paris 1) 96.12, Université Panthéon-Sorbonne (Paris 1).
  5. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 3(4), pages 323-343, December.
  6. Antoine Billot & Alain Chateauneuf & Itzhak Gilboa & Jean-Marc Tallon, 2000. "Sharing beliefs: between agreeing and disagreeing," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00174553, HAL.
  7. Dow, James & Werlang, Sergio Ribeiro da Costa, 1992. "Uncertainty Aversion, Risk Aversion, and the Optimal Choice of Portfolio," Econometrica, Econometric Society, Econometric Society, vol. 60(1), pages 197-204, January.
  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, Elsevier, vol. 22(3), pages 357-368, March.
  10. Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, Econometric Society, vol. 62(2), pages 283-322, March.
  11. Malinvaud, E., 1972. "The allocation of individual risks in large markets," Journal of Economic Theory, Elsevier, Elsevier, vol. 4(2), pages 312-328, April.
  12. Malinvaud, E, 1973. "Markets for an Exchange Economy with Individual Risks," Econometrica, Econometric Society, Econometric Society, vol. 41(3), pages 383-410, May.
  13. Karni, Edi & Schmeidler, David, 1991. "Utility theory with uncertainty," Handbook of Mathematical Economics, Elsevier, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 33, pages 1763-1831 Elsevier.
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