The phenomena of ambiguity and ambiguity aversion, introduced in Daniel Ellsberg’s seminal 1961 article, are ubiquitous in the real-world and violate both the key rationality axioms and classic models of choice under uncertainty. In particular, they violate the hypothesis that individuals’ uncertain beliefs can be represented by subjective probabilities (sometimes called personal probabilities or priors). This chapter begins with a review of early notions of subjective probability and Leonard Savage’s joint axiomatic formalization of expected utility and subjective probability. It goes on to describe Ellsberg’s classic urn paradoxes and the extensive experimental literature they have inspired. It continues with analytical descriptions of the numerous (primarily axiomatic) models of ambiguity aversion which have been developed by economic theorists, and concludes with a discussion of some current theoretical topics and newer

A two-parameter model of dispersion aversion. The idea of representing choice under uncertainty as a trade-off between mean returns and some measure of risk or uncertainty is fundamental to the analysis of investment decisions. In this paper, we show that preferences can be characterized in this way, even in the absence of objective probabilities. We develop a model of uncertainty averse preferences that is based on a mean and a measure of the dispersion of the state-wise utility of an act. The dispersion measure exhibits positive linear homogeneity, sub-additivity, translation invariance and complementary symmetry. Since preferences are only weakly separable in terms of these two summary statistics, the uncertainty premium need not be constant. We show that the standard results originally derived in the context of mean-variance analysis and expected utility theory apply in this more generally setting. In particular, we generalize the concept of decreasing absolute risk aversion and show that the usual comparative static results from EU theory remain valid. Further we derive two-fund separation and asset pricing results analogous to those that hold for the standard CAPM.

ABSTRACT. Classical mean variance utility of Markowitz [1952] and Tobin [1958] have relied on objective expected utility hypothesis. This paper presents a choice-based axiomatization of mean variance utility, in a Savage-type setting of ambiguity, which neither assumes nor implies that individual’s preferences over portfolios conform to the expected utility hypothesis.

This paper axiomatizes a class of preferences displaying decreasing absolute uncer-tainty aversion, which allows a decision maker to be more willing to take uncertainty-bearing behavior when he becomes wealthier. In our first main result, we obtain three equivalent representations. The first is a variation on the constraint criterion of Hansen and Sargent (2001). The other two generalize Gilboa and Schmeidler (1989)’s maxmin criterion and Maccheroni, Marinacci and Rustichini (2006)’s variational representation. This class, when restricted to preferences exhibiting constant absolute uncertainty aversion, is exactly Maccheroni, Marinacci and Rustichini (2006)’s variational prefer-ences. In our second main result, we establish relationships among the representations for several important classes within variational preferences. 1

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