Diversification, convex preferences and non-empty core in the Choquet expected utility model |
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Authors: | Alain Chateauneuf Jean-Marc Tallon |
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Affiliation: | CERMSEM, Université Paris I Panthéon-Sorbonne, 106-112, Bd de l'H?pital,75647 Paris Cedex 13, FRANCE (e-mail: chateaun@univ-paris1.fr), FR EUREQua, CNRS-Université Paris I Panthéon-Sorbonne, 106-112, Bd de l'H?pital,75647 Paris Cedex 13, FRANCE (e-mail: jmtallon@univ-paris1.fr), FR
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Abstract: | Summary. 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. Received: July 27, 1999; revised version: November 7, 2000 |
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Keywords: | and Phrases: Diversification Choquet expected utility Capacity Convex preferences Core. |
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