Higher-Order Stochastic Dominance Constraints in Optimization

This contribution examines optimization problems that involve stochastic dominance constraints. These problems have uncountably many constraints. We develop methods for verifying stochastic dominance by reducing the constraints to a set of test points which is at most countable. This improves both theoretical understanding and computational efficiency. Our approach introduces two formulations of stochastic dominance–one employs expectation operators and another based on risk measures–allowing for efficient verification approaches. Additionally, we develop an optimization framework incorporating these stochastic dominance constraints. Numerical results validate the effectiveness of our method, showcasing by solving higher-order stochastic dominance problems, with applications to fields such as portfolio optimization.