Sample Out-of-Sample Inference Based on Wasserstein Distance
作者研究如何将金融机构和监管机构各自使用的不确定性模型纳入统一框架。金融机构根据自身模型做决策，而监管机构用另一模型评估风险，两者可能不同。作者引入一个对抗性角色，该角色在预算约束下，用监管机构的情景替换金融机构生成的情景，替换成本由Wasserstein距离（一种衡量两个概率分布差异的统计方法）度量。作者还利用统计理论，在双方样本量都很大时，对估计误差的大小进行推断。该框架在分布鲁棒优化（一种完美信息博弈，决策者对抗扰动基准分布的对手）的背景下得到更广泛的阐释。
Financial institutions make decisions according to a model of uncertainty. At the same time, regulators often evaluate the risk exposure of these institutions using a model of uncertainty, which is often different from the one used by the institutions. How can one incorporate both views into a single framework? This paper provides such a framework. It quantifies the impact of the misspecification inherent to the financial institution data-driven model via the introduction of an adversarial player. The adversary replaces the institution's generated scenarios by the regulator's scenarios subject to a budget constraint and a cost that measures the distance between the two sets of scenarios (using what in statistics is known as the Wasserstein distance). This paper also harnesses statistical theory to make inference about the size of the estimated error when the sample sizes (both of the institution and the regulator) are large. The framework is explained more broadly in the context of distributionally robust optimization (a class of perfect information games, in which decisions are taken against an adversary that perturbs a baseline distribution).