Higher-Order Stochastic Dominance Constraints in Optimization

Abstract: This contribution examines optimization problems that involve stochastic dominance constraints. These problems have uncountably many constraints. We develop methods to solve the optimization problem by reducing the constraints to a finite set of test points needed to verify stochastic dominance. This improves both theoretical understanding and computational efficiency. Our approach introduces two formulations of stochastic dominance$\unicode{x2013}$one employs expectation operators and another based on risk measures$\unicode{x2013}$allowing for efficient verification processes. Additionally, we develop an optimization framework incorporating these stochastic dominance constraints. Numerical results validate the robustness of our method, showcasing its effectiveness for solving higher-order stochastic dominance problems, with applications to fields such as portfolio optimization.