Quantifying Distributional Model Risk via Optimal Transport

• 成果类型: Article
• 署名作者: Blanchet, Jose; Murthy, Karthyek
• 署名单位: Stanford University; Singapore University of Technology & Design
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2018.0936
• 发表日期: 2019
• 页码: 565-600
• 关键词: sensitivity-analysis; robust optimization; CONVERGENCE; uncertainty; distance; bounds

摘要

This paper deals with the problem of quantifying the impact of model mis-specification when computing general expected values of interest. The methodology that we propose is applicable in great generality; in particular, we provide examples involving path-dependent expectations of stochastic processes. Our approach consists of computing bounds for the expectation of interest regardless of the probability measure used, as long as the measure lies within a prescribed tolerance measured in terms of a flexible class of distances from a suitable baseline model. These distances, based on optimal transportation between probability measures, include Wasserstein's distances as particular cases. The proposed methodology is well suited for risk analysis and distributionally robust optimization, as we demonstrate with applications. We also discuss how to estimate the tolerance region nonparametrically using Skorokhod-type embeddings in some of these applications.