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

TL;DR

This paper develops a distributionally robust optimization framework with second-order stochastic dominance constraints using Wasserstein balls, providing convergent approximation methods and demonstrating effectiveness in portfolio selection.

Contribution

It introduces a novel split-and-dual decomposition framework for robust stochastic dominance constrained optimization under Wasserstein ambiguity sets.

Findings

The linear programming lower bound accurately approximates the problem.

The proposed upper bound converges under certain conditions.

Numerical experiments validate the effectiveness of the methods in portfolio optimization.

Abstract

We consider a distributionally robust second-order stochastic dominance constrained optimization problem. We require the dominance constraints 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 convergency for both lower and upper approximations given some constraint qualification conditions. 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 convergency and effectiveness of the proposed two approximation methods.