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).

Economists routinely make functional form assumptions on demand curves to derive welfare conclusions. How sensitive are these conclusions to such assumptions? In this paper, we develop robustness measures that quantify the extent to which the true demand curve must deviate from common functional form assumptions in order to overturn a welfare conclusion. We parametrize this variability in terms of the gradient and curvature of the demand curve. By leveraging tools from information design, we show that our measures are easy to compute. Our measures are also flexible and easy to use, as we illustrate through empirical applications. (JEL D01, D60, F13, H55, Q48)