Decision Making Under Model Uncertainty: Fréchet–Wasserstein Mean Preferences

This paper contributes to the literature on decision making under multiple probability models by studying a class of variational preferences. These preferences are defined in terms of Fréchet mean utility functionals, which are based on the Wasserstein metric in the space of probability models. In order to produce a measure that is the “closest” to all probability models in the given set, we find the barycenter of the set. We derive explicit expressions for the Fréchet–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 the model that maximizes the probability that different decision makers will agree on, which could be useful for designing and pricing a catastrophe bond. This paper was accepted by Manel Baucells, decision analysis.

Robust Decision Theory and Econometrics

This review uses the empirical analysis of portfolio choice to illustrate econometric issues that arise in decision problems. Subjective expected utility (SEU) can provide normative guidance to an investor making a portfolio choice. The investor, however, may have doubts on the specification of the distribution and may seek a decision theory that is less sensitive to the specification. I consider three such theories: maxmin expected utility, variational preferences (including multiplier and divergence preferences and the associated constraint preferences), and smooth ambiguity preferences. I use a simple two-period model to illustrate their application. Normative empirical work on portfolio choice is mainly in the SEU framework, and bringing in ideas from robust decision theory may be fruitful.

Ambiguity Models and the Machina Paradoxes

Machina (2009) introduced two examples that falsify Choquet expected utility, presently one of the most popular models of ambiguity. This article shows that Machina's examples falsify not only the model mentioned, but also four other popular models for ambiguity of the literature, namely maxmin expected utility, variational preferences, α-maxmin, and the smooth model of ambiguity aversion. Thus, Machina's examples pose a challenge to most of the present field of ambiguity. Finally, the paper discusses how an alternative representation of ambiguity-averse preferences works to accommodate the Machina paradoxes and what drives the results. (JEL D81)