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Diversification, convex preferences and non-empty core in the Choquet expected utility model

Author

Listed:
  • Jean-Marc Tallon

    () (EUREQua, CNRS-Université Paris I Panthéon-Sorbonne, 106-112, Bd de l'Hôpital,75647 Paris Cedex 13, FRANCE)

  • Alain Chateauneuf

    () (CERMSEM, Université Paris I Panthéon-Sorbonne, 106-112, Bd de l'Hôpital,75647 Paris Cedex 13, FRANCE)

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, which is itself equivalent to the notion of comonotone diversification, that we introduce. In an Anscombe-Aumann setting, preference for diversification is equivalent to convexity of the capacity and preference for sure diversification is equivalent to non-empty core. In the expected utility model, all these notions of diversification are equivalent and are represented by the concavity of the utility index.

Suggested Citation

  • Jean-Marc Tallon & Alain Chateauneuf, 2002. "Diversification, convex preferences and non-empty core in the Choquet expected utility model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 19(3), pages 509-523.
    • Handle: RePEc:spr:joecth:v:19:y:2002:i:3:p:509-523
    Note: Received: July 27, 1999; revised version: November 7, 2000
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