We derive the analogue of the classic Arrow-Pratt approximation of the certainty equivalent under model uncertainty as de…ned by the smooth model of decision making under ambiguity of Klibano¤, Marinacci and Mukerji (2005).We study its scope via a portfolio allocation exercise that delivers a tractable mean-variance model adjusted for model uncertainty.In a problem with a risk-free asset, a risky asset, and an ambiguous asset, we …nd that portfolio rebalancing in response to higher model uncertainty only depends on the ambiguous asset's alpha, setting the performance of the risky asset as benchmark.In addition, the portfolios recommended by our model are not systematically conservative on the share held in the ambiguous asset: indeed, in general, it is not true that greater ambiguity reduces the optimal demand for the ambiguous asset.The analytical tractability of the enhanced Arrow-Pratt approximation renders our model especially well suited for calibration exercises aimed at exploring the consequences of ambiguity aversion on equilibrium asset prices."Crises feed uncertainty.

We characterize, in the Anscombe–Aumann framework, the preferences for which there are a utility functionu on outcomes and an ambiguity indexc on the set of probabilities on the states of the world such that, for all acts f and g, . The function u represents the decision maker's risk attitudes, while the index c captures his ambiguity attitudes. These preferences include the multiple priors preferences of Gilboa and Schmeidler and the multiplier preferences of Hansen and Sargent. This provides a rigorous decision-theoretic foundation for the latter model, which has been widely used in macroeconomics and finance.

A decision maker (DM) is characterized by two binary relations. The first reflects choices that are rational in an “objective” sense: the DM can convince others that she is right in making them. The second relation models choices that are rational in a “subjective” sense: the DM cannot be convinced that she is wrong in making them. In the context of decision under uncertainty, we propose axioms that the two notions of rationality might satisfy. These axioms allow a joint representation by a single set of prior probabilities and a single utility index. It is “objectively rational” to choose f in the presence of g if and only if the expected utility of f is at least as high as that of g given each and every prior in the set. It is “subjectively rational” to choose f rather than g if and only if the minimal expected utility of f (with respect to all priors in the set) is at least as high as that of g. In other words, the objective and subjective rationality relations admit, respectively, a representation à la Bewley (2002) and à la Gilboa and Schmeidler (1989). Our results thus provide a bridge between these two classic models, as well as a novel foundation for the latter.

We provide a behavioral foundation to the notion of 'mixture' of acts, which is used to great advantage in the decision setting introduced by Anscombe and Aumann. Our construction allows one to formulate mixture-space axioms even in a fully subjective setting, without assuming the existence of randomizing devices. This simplifies the task of developing axiomatic models which only use behavioral data. Moreover, it is immune from the difficulty that agents may 'distort' the probabilities associated with randomizing devices. For illustration, we present simple subjective axiomatizations of some models of choice under uncertainty, including the maxmin expected utility model of Gilboa and Schmeidler, and Bewley's model of choice with incomplete preferences.