This chapter of a collective book aims at presenting the basics of decision making under risk. We first define notions of risk and increasing risk and recall definitions and classifications (that are valid independently of any representation) of behavior under risk. We then review the classical...

This paper explores risk-sharing and equilibrium in a general equilibrium set-up wherein agents are non-additive expected utility maximizers. We show that when agents have the same convex capacity, the set of Pareto-optima is independent of it and identical to the set of optima of an economy in...

Tribute to Jean-Yves Jaffray by the French Group of Decision Theory

We show that when decision makers are of the multiple prior kind, there is an equivalence between no betting and non empty intersection of the sets of priors.

This paper explores risk-sharing and equilibrium in a general equilibrium set-up wherein agents are non-additive expected utility maximizers. We show that when agents have the same convex capacity, the set of Pareto-optima is independent of it and identical to the set of optima of an economy in...

We show that the monotone continuity condition introduced by Villegas (1964) and Arrow (1970) is the behavioral counterpart of countable additivity (and relative weak compactness) in a multiple priors model. This generalizes their original result, in which the special case of a singleton set of...

In a multiple priors model á la Gilboa and Schmeidler (1989), we provide necessary and sufficient behavioral conditions ensuring the countable additivity and non-atomicity of all priors. Copyright Springer-Verlag Berlin/Heidelberg 2005

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...