  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.
