This paper studies distributional model risk in marginal problems, where each marginal measure is assumed to lie in a Wasserstein ball centered at a fixed reference measure with a given radius. Theoretically, we establish several fundamental results including strong duality, finiteness of the proposed Wasserstein distributional model risk, and the existence of an optimizer at each radius. In addition, we show continuity of the Wasserstein distributional model risk as a function of the radius. Using strong duality, we extend the well-known Makarov bounds for the distribution function of the sum of two random variables with given marginals to Wasserstein distributionally robust Markarov bounds. Practically, we illustrate our results on four distinct applications when the sample information comes from multiple data sources and only some marginal reference measures are identified. They are: partial identification of treatment effects; externally valid treatment choice via robust welfare functions; Wasserstein distributionally robust estimation under data combination; and evaluation of the worst aggregate risk measures.

翻译：本文研究边际问题中的分布模型风险，其中每个边际测度假设位于以固定参考测度为中心、给定半径的Wasserstein球内。理论上，我们建立了若干基础性结果，包括强对偶性、所提Wasserstein分布模型风险的有限性，以及每个半径下最优解的存在性。此外，我们证明了Wasserstein分布模型风险作为半径函数的连续性。利用强对偶性，我们将经典的给定边际下两个随机变量之和分布函数的Makarov界推广至Wasserstein分布稳健Makarov界。实际应用中，当样本信息来自多个数据源且仅识别部分边际参考测度时，我们通过四个不同应用场景展示了结果：处理效应的局部识别；基于稳健福利函数的外部有效处理选择；数据组合下的Wasserstein分布稳健估计；以及最差聚合风险测度的评估。