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Diversification, Convex Preferences and Non-Empty Core

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  • Alain Chateauneuf

    (CERMSEM)

  • Jean-Marc Tallon

    (Universite Paris 1)

Abstract

We show, in the Choquet expected utility model, that preference for diversification, that is, convex preferences, is equivalent to a concave utility index and a convex capacity. We then introduce a weaker notion of diversification, namely ``sure diversification.'' We show that this implies that the core of the capacity is non-empty. The converse holds under concavity of the utility index. This property is shown to be equivalent to the notion of comonotone diversification\,; notion that we introduce in the paper. Finally, in the expected utility model, all these notions of diversification are equivalent and are represented by the concavity of the utility index.

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 0751.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:0751

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  1. Chateauneuf, Alain & Dana, Rose-Anne & Tallon, Jean-Marc, 2000. "Optimal risk-sharing rules and equilibria with Choquet-expected-utility," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 191-214, October.
  2. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  3. Larry Epstein, 1997. "Uncertainty Aversion," Working Papers epstein-97-01, University of Toronto, Department of Economics.
  4. Dekel, Eddie, 1989. "Asset Demands without the Independence Axiom," Econometrica, Econometric Society, vol. 57(1), pages 163-69, January.
  5. Gerard Debreu & Tjalling C. Koopmans, 1980. "Additively Decomposed Quasiconvex Functions," Cowles Foundation Discussion Papers 574, Cowles Foundation for Research in Economics, Yale University.
  6. 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.
  7. Wakker, Peter, 1990. "Characterizing optimism and pessimism directly through comonotonicity," Journal of Economic Theory, Elsevier, vol. 52(2), pages 453-463, December.
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Cited by:
  1. Chateauneuf, Alain & Dana, Rose-Anne & Tallon, Jean-Marc, 2000. "Optimal risk-sharing rules and equilibria with Choquet-expected-utility," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 191-214, October.
  2. Chateauneuf, A. & Grabisch, M. & Rico, A., 2008. "Modeling attitudes toward uncertainty through the use of the Sugeno integral," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1084-1099, December.
  3. repec:hal:journl:halshs-00451997 is not listed on IDEAS
  4. Alain Chateauneuf & Ghizlane Lakhnati, 2007. "From sure to strong diversification," Economic Theory, Springer, vol. 32(3), pages 511-522, September.
  5. Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Levine's Working Paper Archive 7616, David K. Levine.
  6. Borglin, Anders & Flåm, Sjur, 2007. "Rationalizing Constrained Contingent Claims," Working Papers 2007:12, Lund University, Department of Economics.
  7. repec:hal:journl:halshs-00174770 is not listed on IDEAS

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