Simone Cerreia-Vioglio

Ambiguity and robust statistics

Starting with the seminal paper of Gilboa and Schmeidler (1989) [32] an analogy between the maxmin approach of decision theory under ambiguity and the minimax approach of robust statistics – e.g., Blum and Rosenblatt (1967) [10] – has been hinted at. The present paper formally clarifies this relation by showing the conditions under which the two approaches are actually equivalent.

Classical subjective expected utility

We consider decision makers who know that payoff-relevant observations are generated by a process that belongs to a given class M, as postulated in Wald [Wald A (1950) Statistical Decision Functions (Wiley, New York)]. We incorporate this Waldean piece of objective information within an otherwise subjective setting à la Savage [Savage LJ (1954) The Foundations of Statistics (Wiley, New York)] and show that this leads to a two-stage subjective expected utility model that accounts for both state and model uncertainty.

Objective rationality and uncertainty averse preferences

We provide a bridge between Bewley preferences [2] and Uncertainty averse preferences [4]. In doing this, we generalize the ?ndings of Gilboa, Maccheroni, Marinacci, and Schmeidler [11]. To exemplify this new framework, we then study a class of preferences that we call Constrained Multiplier preferences and that was ?rst proposed by Wang [19].

Put-Call Parity and Market Frictions

We extend the Fundamental Theorem of Finance and the Pricing Rule Representation Theorem to the case in which market frictions are taken into account but the Put–Call Parity is still assumed to hold. In turn, we obtain a representation of the pricing rule as a discounted expectation with respect to a nonadditive risk neutral probability.

A Note on Comparative Ambiguity Aversion and Justifiability

We consider a decision maker who ranks actions according to the smooth ambiguity criterion of Klibanos et al. (2005). An action is justifiable if it is a best reply to some belief over probabilistic models. We show that higher ambiguity aversion expands the set of justifiable actions. In turn, this implies that higher ambiguity aversion expands the set of rationalizable actions of a game. Our results follow from a generalization of the duality lemma of Wald (1949) and Pearce (1984).

Stochastic Dominance Analysis Without the Independence Axiom

We characterize the consistency of a large class of nonexpected utility preferences (including mean-variance preferences and prospect theory preferences) with stochastic orders (for example, stochastic dominances of different degrees). Our characterization rests on a novel decision theoretic result that provides a behavioral interpretation of the set of all derivatives of the functional representing the decision maker’s preferences. As an illustration, we consider in some detail prospect theory and choice-acclimating preferences, two popular models of reference dependence under risk, and we show the incompatibility of loss aversion with prudence. This paper was accepted by James Smith, decision analysis.