Decision Making Under Model Uncertainty: Fréchet–Wasserstein Mean Preferences

Abstract. This paper contributes to the literature on decision making under multiple probabilitymodels by studying a class of variational preferences. These preferences are defined in terms of Fr echet mean utility functionals, which are based on the Wasserstein metric in the space of probabilitymodels. In order to produce ameasure that is the “closest” to all probabilitymodels in the given set,we find the barycenter of the set. We derive explicit expressions for the Fr echet–Wasserstein mean utility functionals and show that they can be expressed in terms of an expansion that provides a tractable link between risk aversion and ambiguity aversion. The proposed utility functionals are illustrated in terms of two applications. The first application allows us to define the social discount rate under model uncertainty. In the second application, the functionals are used in risk securitization. The barycenter in this case can be interpreted as themodel thatmaximizes the probability that different decisionmakers will agree on,which could be useful for designing and pricing a catastrophe bond.