Decision Making Under Model Uncertainty: Fréchet–Wasserstein Mean Preferences
研究在多个概率模型下决策的一类变分偏好，基于瓦瑟斯坦度量定义弗雷歇均值效用泛函，推导其表达式并展示在确定社会贴现率和风险证券化中的应用。
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.