Distributionally Robust Second-Order Stochastic Dominance Constrained Optimization with Wasserstein Ball
研究在Wasserstein球内所有概率分布下满足二阶随机占优约束的优化问题，提出线性规划下界和分裂对偶分解上界两种近似方法，并验证其在投资组合选择中的有效性。
We consider a distributionally robust second-order stochastic dominance constrained optimization problem. We require the dominance constraints to hold with respect to all probability distributions in a Wasserstein ball centered at the empirical distribution. We adopt the sample approximation approach 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 establish quantitative convergence for both lower and upper approximations given some constraint qualification conditions. To efficiently solve the nonconvex upper bound problem, we use a sequential convex approximation algorithm. Numerical evidence on a portfolio selection problem validates the convergence and effectiveness of the proposed two approximation methods.