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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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References

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  1. Tallon, Jean-Marc & Dana, Rose-Anne & Chateauneuf, Alain, 2000. "Optimal risk-sharing rules and equilibria with Choquet-expected-utility," Open Access publications from Université Paris-Dauphine urn:hdl:123456789/5461, Université Paris-Dauphine.
  2. Dekel, Eddie, 1989. "Asset Demands without the Independence Axiom," Econometrica, Econometric Society, vol. 57(1), pages 163-69, January.
  3. 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.
  4. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  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. Larry Epstein, 1997. "Uncertainty Aversion," Working Papers epstein-97-01, University of Toronto, Department of Economics.
  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. Paolo Ghirardato & Massimo Marinacci, 2000. "Risk, Ambiguity, and the Separation of Utility and Beliefs," Levine's Working Paper Archive 7616, David K. Levine.
  2. 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.
  3. 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.
  4. Borglin, Anders & Flåm, Sjur, 2007. "Rationalizing Constrained Contingent Claims," Working Papers 2007:12, Lund University, Department of Economics.
  5. Alain Chateauneuf & Ghizlane Lakhnati, 2007. "From sure to strong diversification," Economic Theory, Springer, vol. 32(3), pages 511-522, September.
  6. Denuit, M & Dhaene, Jan & Goovaerts, Marc & Kaas, R & Laeven, R, 2005. "Risk measurement with the equivalent utility principles," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/122216, Katholieke Universiteit Leuven.
  7. Wakker, Peter P., 2005. "Decision-foundations for properties of nonadditive measures: general state spaces or general outcome spaces," Games and Economic Behavior, Elsevier, vol. 50(1), pages 107-125, January.
  8. Kobberling, Veronika & Wakker, Peter P., 2005. "An index of loss aversion," Journal of Economic Theory, Elsevier, vol. 122(1), pages 119-131, May.

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