Optimal risk-sharing rules and equilibria with Choquet-expected-utility
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.
|Date of creation:||2000|
|Publication status:||Published in Journal of Mathematical Economics, Elsevier, 2000, 34 (2), pp.191-214. <10.1016/S0304-4068(00)00041-0>|
|Note:||View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00451997|
|Contact details of provider:|| Web page: https://hal.archives-ouvertes.fr/|
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- Tallon, J.-M. & Chateauneuf, A., 1998.
"Diversification, Convex Preferences and Non-Empty Core,"
Papiers d'Economie MathÃ©matique et Applications
98.32, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).
- Alain Chateauneuf & Jean-Marc Tallon, 2000. "Diversification, Convex Preferences and Non-Empty Core," Econometric Society World Congress 2000 Contributed Papers 0751, Econometric Society.
- Antoine Billot & Alain Chateauneuf & Itzhak Gilboa & Jean-Marc Tallon, 2000.
"Sharing Beliefs: Between Agreeing and Disagreeing,"
Econometric Society, vol. 68(3), pages 685-694, May.
- Billot, A. & Chateauneuf, A. & Gilboa, I. & Tallon, J.-M., 1998. "Sharing Beliefs: Between Agreeing and Disagreeing," Papiers d'Economie MathÃ©matique et Applications 98.30, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).
- Itzhak Gilboa & Antoine Billot & Alain Chateauneuf & Jean-Marc Tallon, 2000. "Sharing Beliefs: between Agreeing and Disagreeing," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00753122, HAL.
- 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.
- Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
- 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.
- 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.
- 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.
- repec:adr:anecst:y:1997:i:48:p:10 is not listed on IDEAS
- Jean-Marc Tallon, 1998.
"Do sunspots matter when agents are Choquet-expected-utility maximizers?,"
- 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.
- Malinvaud, E, 1973. "Markets for an Exchange Economy with Individual Risks," Econometrica, Econometric Society, vol. 41(3), pages 383-410, May.
- David Schmeidler, 1989.
"Subjective Probability and Expected Utility without Additivity,"
Levine's Working Paper Archive
7662, David K. Levine.
- Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
- Epstein, Larry G & Wang, Tan, 1994. "Intertemporal Asset Pricing Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 62(2), pages 283-322, March.
- 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.
- Malinvaud, E., 1972. "The allocation of individual risks in large markets," Journal of Economic Theory, Elsevier, vol. 4(2), pages 312-328, April.
- Cass, David & Chichilnisky, Graciela & Wu, Ho-Mou, 1996. "Individual Risk and Mutual Insurance," Econometrica, Econometric Society, vol. 64(2), pages 333-341, March.
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