We study the cores of non-atomic market games, a class of transferable utility co- operative games introduced by Aumann and Shapley [2], and, more in general, of those games that admit a na-continuous and concave extension to the set of ideal coalitions, studied by Einy, Moreno, and Shitovitz...

Concavity and supermodularity are in general independent properties. A class of functionals defined on a lattice cone of a Riesz space has the Choquet property when it is the case that its members are concave whenever they are supermodular. We show that for some important Riesz spaces both the...

When there is uncertainty about interest rates (typically due to either illiquidity or defaultability of zero coupon bonds) the cash- additivity assumption on risk measures becomes problematic. When this assumption is weakened, to cash-subadditivity for example, the equivalence between convexity...

We introduce a notion of complete monotone quasiconcave duality and we show that it holds for important classes of quasiconcave functions.

We study uncertainty averse preferences, that is, complete and transitive preferences that are convex and monotone. We establish a representation result, which is at same time general and rich in structure. Many objective functions commonly used in applications are special cases of this...

We study unique and globally attracting solutions of a general nonlinear equation that has as special cases some recursive equations widely used in Economics.

We consider decision makers that know that payo¤ relevant observations are generated by a process that belongs to a given class M, as postulated in Wald [33]. We incorporate this Waldean piece of objective information within an otherwise subjective setting a la Savage [30] and show that this...

We give a general integral representation theorem (Theorem 6) for nonadditive functionals de?ned on an Archimedean Riesz space X with order unit. Additivity is replaced by a weak form of modularity, or equivalently dual comonotonic additivity, and integrals are Choquet integrals. Those integrals...

We introduce and study finitely well-positioned sets, a class of asymptotically “narrow” sets that generalize the well-positioned sets recently investigated by Adly, Ernst and Thera in [1] and [3], as well as the plastering property of Krasnoselskii.

Starting with the seminal paper of Gilboa and Schmeidler (1989) an analogy between the maxmin approach of Decision Theory under Ambiguity and the minimax approach of Robust Statistics -- e.g. Huber and Strassen (1973) -- has been hinted at. The present paper formally clarifies this relation by...