Dual Utilities on Risk Aggregation under Dependence Uncertainty

Finding the worst-case value of a preference over a set of plausible models is a well-established approach to address the issue of model uncertainty or ambiguity. In this paper, we study the worst-case evaluation of Yaari dual utility functionals of an aggregate risk under dependence uncertainty along with its decision-theoretic implications. To arrive at our main findings, we introduce a technical notion of conditional joint mixability. Lower and upper bounds on dual utilities with dependence uncertainty are established, and in the presence of conditional joint mixability, they are shown to be exact bounds. Moreover, conditional joint mixability is indeed necessary for attaining these exact bounds when the distortion functions are strictly inverse-S-shaped. A particular economic implication of our results is what we call the pessimism effect. We show that a (generally non-convex/non-concave) dual utility-based decision maker under dependence uncertainty behaves as if she had a risk-averse dual utility which is more pessimistic but free of dependence uncertainty.