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Distributionally robust second-order stochastic dominance constrained optimization with Wasserstein distance

Yu Mei (meiyu414***at***stu.xjtu.edu.cn)
Jia Liu (jialiu***at***xjtu.edu.cn)
Zhiping Chen (zchen***at***mail.xjtu.edu.cn)

Abstract: We consider a distributionally robust second-order stochastic dominance constrained optimization problem, where the true distribution of the uncertain parameters is ambiguous. The ambiguity set contains all probability distributions close to the empirical distribution under the Wasserstein distance. We adopt the sample approximation technique to develop a linear programming formulation that provides a lower bound. We propose a novel split-and-dual decomposition framework which provides an upper bound. We prove that both lower and upper bound approximations are asymptotically tight when there are enough samples or pieces. We present quantitative error estimation for the upper bound under a specific constraint qualification condition. To efficiently solve the non-convex upper bound problem, we use a sequential convex approximation algorithm. Numerical evidences on a portfolio selection problem valid the efficiency and asymptotically tightness of the proposed two approximation methods.

Keywords: stochastic dominance; distributionally robust optimization; Wasserstein distance; sequential convex approximation

Category 1: Robust Optimization

Citation:

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Entry Submitted: 01/03/2021
Entry Accepted: 01/03/2021
Entry Last Modified: 01/04/2021

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