Ergodic Theorems for Lower Probabilities

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

Risk Measures: Rationality and Diversification

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 and the diversication principle no longer holds. In fact, this principle only implies (and it is implied by) quasiconvexity. For this reason, in this paper quasiconvex risk measures are studied. We provide a dual characterization of quasiconvex cash-subadditive risk measures and we establish necessary and sufficient conditions for their law invariance. As a byproduct, we obtain an alternative characterization of the actuarial mean value premium principle.Risk Measures, Diversification, Cash-subadditivity, Quasiconvexity, Law-invariance, Mean Value Premium Principle

Complete Monotone Quasiconcave Duality

We introduce a notion of complete monotone quasiconcave duality and we show that it holds for important classes of quasiconcave functions.Quasiconcavity, Quasiconvexity, Duality, Indirect Utility

Uncertainty Averse Preferences

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 representation.ambiguity aversion, games against nature, model uncertainty, smooth ambiguity preferences, variational preferences

Probabilistic Sophistication, Second Order Stochastic Dominance, and Uncertainty Aversion

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 satisfy second order stochastic dominance, as well as uncertainty averse preferences that are probabilistically sophisticated.Probabilistic Sophistication; Second Order Stochastic Dominance; Uncertainty Aversion; Unambiguous Events; Subjective Expected Utility

Equilibria of nonatomic anonymous games

We define a new notion of equilibrium for nonatomic anonymous games, termed epsilon-estimated equilibrium, and prove its existence for any positive s. This notion encompasses and brings to nonatomic games recent concepts of equilibrium such as self-confirming, peer-confirming, and Berk-Nash. This augmented scope is our main motivation. Our approach also resolves some conceptual problems present in Schmeidler (1973) pointed out by Shapley

Rational Preferences under Ambiguity

This paper analyzes preferences in the presence of ambiguity that are rational in the sense of satisfying the classical ordering condition as well as monotonicity. Under technical conditions that are natural in an Anscombe-Aumann environment, we show that even for such general preference model it is possible to identify a set of priors, as first envisioned by Ellsberg (1961). We then discuss ambiguity attitudes, as well as unambiguous acts and events, for the class of rational preferences we consider.Rational Preferences; Ambiguity; Unambiguous Acts and Events