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.

Abstract We provide two characterizations, one axiomatic and the other neuro-computational, of the dependence of choice probabilities on deadlines, within the widely used softmax representation $$\beginalign* p_t\left( a,A\right) =\dfrace^\fracu\left( a\right) λ\left( t\right) +α\left( a\right) \sum_b\in Ae^\fracu\left( b\right) λ\left( t\right) +α\left( b\right) , \endalign*$$ where $p_t\left( a,A\right)$ is the probability that alternative a is selected from the set A of feasible alternatives if t is the time available to decide, λ is a time-dependent noise parameter measuring the unit cost of information, u is a time-independent utility function, and α is an alternative-specific bias that determines the initial choice probabilities (reflecting prior information and memory anchoring). Our axiomatic analysis provides a behavioural foundation of softmax (also known as Multinomial Logit Model when α is constant). Our neuro-computational derivation provides a biologically inspired algorithm that may explain the emergence of softmax in choice behaviour. Jointly, the two approaches provide a thorough understanding of softmaximization in terms of internal causes (neuro-physiological mechanisms) and external effects (testable implications).

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.

Abstract We use decision theory to confront uncertainty that is sufficiently broad to incorporate “models as approximations.” We presume the existence of a featured collection of what we call “structured models” that have explicit substantive motivations. The decision-maker confronts uncertainty through the lens of these models, but also views these models as simplifications, and hence, as misspecified. We extend the max–min analysis under model ambiguity to incorporate the uncertainty induced by acknowledging that the models used in decision making are simplified approximations. Formally, we provide an axiomatic rationale for a decision criterion that incorporates model misspecification concerns. We then extend our analysis beyond the max-min case allowing for a more general criterion that encompasses a Bayesian formulation.

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, an agent learns the implied distribution of payoffs, but alternative strategies yield payoffs with unknown distributions; increased aversion to ambiguity makes such strategies less appealing. In sum, a kind of “status quo bias” emerges; in the long run, the uncertainty related to tested strategies disappears, but the uncertainty implied by the untested ones does not. (JEL C72, C73, D81, D83)

We provide a new foundation of risk aversion by showing that this attitude is fully captured by the propensity to seize insurance opportunities. In our main results, we first characterize Arrow-Pratt (1963–1964) risk aversion in terms of propensity to full insurance and the stronger notion of risk aversion of Rothschild and Stiglitz (1970) in terms of propensity to partial insurance. We then extend the analysis to comparative risk aversion by showing that the classical notion of Yaari (1969) corresponds to comparative propensity to full insurance, while the stronger notion of Ross (1981) corresponds to comparative propensity to partial insurance. (JEL D81, G22, G52)