In a decision problem under uncertainty, a decision maker considers a set of alternative actions whose consequences depend on uncertain factors outside his control. Following Luce and Raiffa (1957), we adopt a natural representation of such situation that takes as primitives a set of conceivable...

Given a functional defi?ned on a nonempty subset of an Archimedean Riesz space with unit, necessary and sufficient conditions are obtained for the existence of a (convex or concave) niveloid that extends the functional to the entire space. In the language of mathematical fi?nance, this problem...

We study the interplay of probabilistic sophistication, second order stochastic dominance and uncertainty aversion, three fundamental notions in choice under uncertainty. In particular, our main result, Theorem 2, characterizes uncertainty averse preferences that are probabilistically...

An action is justi?fiable if it is a best reply to some belief. We show that higher ambiguity aversion enlarges the set of justifi?able actions.

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 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...