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We consider a distributionally robust second-order stochastic dominanceconstrained optimization problem. We require the dominance constraints holdwith respect to all probability distributions in a Wasserstein ball centered atthe empirical distribution. We adopt the sample approximation approach todevelop a linear programming formulation that provides a lower bound. Wepropose a novel split-and-dual decomposition framework which provides an upperbound. We establish quantitative convergency for both lower and upperapproximations given some constraint qualification conditions. To efficientlysolve the non-convex upper bound problem, we use a sequential convexapproximation algorithm. Numerical evidences on a portfolio selection problemvalid the convergency and effectiveness of the proposed two approximationmethods.

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