Hyeonseok Park, Assistant Professor of IAER, has his paper accepted for publication in Mathematics of Operations Research. Entitled "Quantifying Distributional Model Risk in Marginal Problems via Optimal Transport", the paper was co-authored Yanqin Fan, Professor of Department of Economics at University of Washington, and Gaoqian Xu, Ph.D. student in Department of Economics at Universtiy of Washington.

This paper studies distributional model risk in marginal problems, where each marginal measure is assumed to lie in a Wasserstein ball. We establish fundamental results including strong duality, finiteness of the proposed Wasserstein distributional model risk, and the existence of an optimizer at each radius. We also 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 Makarov bounds.  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: 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.

Written by:  Hyeonseok Park, Wang Jie

Source:  Institute for Advanced Economic Research