Dual-self Representations of Ambiguity Preferences

Abstract

We propose a class of multiple-prior representations of preferences under ambiguity, where the belief the decision-maker (DM) uses to evaluate an uncertain prospect is the outcome of a game played by two conflicting forces, Pessimism and Optimism. The model does not restrict the sign of the DM's ambiguity attitude, and we show that it provides a unified framework through which to characterize different degrees of ambiguity aversion, and to represent the coexistence of negative and positive ambiguity attitudes within individuals as documented in experiments. We prove that our baseline representation, dual-self expected utility (DSEU), yields a novel representation of the class of invariant biseparable preferences (Ghirardato, Maccheroni, and Marinacci, 2004), which drops uncertainty aversion from maxmin expected utility (Gilboa and Schmeidler, 1989). Extensions of DSEU allow for more general departures from independence.

Star-shaped Risk Measures

“…Indeed, an implication of our main Theorem 5 is that the preferences obtained by replacing uncertainty aversion with increasing relative ambiguity aversion, in the axiom set of[34], are characterized by representation(2). See also Chandrasekher et al[14] for a preference representation which is similar, but where the α a 's are not necessarily grounded, hence they lose the interpretation of action-dependent ambiguity indexes, and increasing relative ambiguity aversion is lost too.…”

“…For instance, Value-at-Risk (VaR) is positively homogeneous without being convex. 14 Specifically, given a probability measure Q, VaR at level β ∈ (0, 1) is defined by…”

“…13 See also Cerreia-Vioglio et al [11]. 14 When we say that a risk measure is "not convex" or "not positively homogeneous" we always mean "in general." 15 ES has been recently given an axiomatic foundation by Wang and Zitikis [45].…”

“…Theorem 5 yields a tractable representation of star-shaped risk measures, and its first use in applications dates back to Castagnoli et al [10]. 21 The special case of coherent risk measures with X = R n also appears in the independent Chandrasekher et al [14].…”

A Theory of Updating Ambiguous Information

“…16 SeeChandrasekher, Frick, Iijima, and Le Yaouanq (2020) for the dual-self expected utility theory. and…”