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...

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.

We propose to bring together two conceptually complementary ideas: (1) selfconfi?rming equilibrium (SCE): at a rest point of learning dynamics in a game played recurrently, agents best respond to confi?rmed beliefs, i.e. beliefs consistent with the evidence they accumulate, and (2) ambiguity...

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 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 extend the Fundamental Theorem of Finance and the Pricing Rule Representation Theorem of Cox and Ross (see Ross [35] and [37] and Cox and Ross [9]) to the case in which market frictions are aken into account but the Put-Call Parity is still assumed to hold. In turn, we obtain a representation...

We analyze a notion of self-confirming equilibrium with non-neutral ambiguity attitudes that generalizes the traditional concept. We show that the set of equilibria expands as ambiguity aversion increases. The intuition is quite simple: by playing the same strategy in a stationary environment,...

We consider real pre-Hilbert modules H on Archimedean f-algebras A with unit e. We provide conditions on A and H such that a Riesz representation theorem for bounded/continuous A-linear operators holds.

We establish an Ergodic Theorem for lower probabilities, a generalization of standard probabilities widely used in applications. As an application, we provide a version for lower probabilities of the Strong Law of Large Numbers.

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...