Diversication, Convex Preferences and Non-empty Core 3 Yz

We show, in the Choquet expected utility model, that preference for diversi cation, that is, convex preferences, is equivalent to a concave utility index and a convex capacity. We then introduce a weaker notion of diversi cation, namely \sure diversication." 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 diversi cation ; notion that we introduce in the paper. Finally, in the expected utility model, all these notions of diversi cation are equivalent and are represented by the concavity of the utility index.