Shortfall-Based Wasserstein Distributionally Robust Optimization

Ruoxuan Li, Wenhua Lv () and Tiantian Mao
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Ruoxuan Li: Department of Statistics and Finance, University of Science and Technology of China, Hefei 230052, China
Wenhua Lv: School of Mathematics and Finance, Chuzhou University, Chuzhou 239000, China
Tiantian Mao: Department of Statistics and Finance, University of Science and Technology of China, Hefei 230052, China

Mathematics, 2023, vol. 11, issue 4, 1-25

Abstract: In this paper, we study a distributionally robust optimization (DRO) problem with affine decision rules. In particular, we construct an ambiguity set based on a new family of Wasserstein metrics, shortfall–Wasserstein metrics, which apply normalized utility-based shortfall risk measures to summarize the transportation cost random variables. In this paper, we demonstrate that the multi-dimensional shortfall–Wasserstein ball can be affinely projected onto a one-dimensional one. A noteworthy result of this reformulation is that our program benefits from finite sample guarantee without a dependence on the dimension of the nominal distribution. This distributionally robust optimization problem also has computational tractability, and we provide a dual formulation and verify the strong duality that enables a direct and concise reformulation of this problem. Our results offer a new DRO framework that can be applied in numerous contexts such as regression and portfolio optimization.

Keywords: distributionally robust optimization; Wasserstein metrics; utility-based shortfall risk measures (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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