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 dominanceone employs expectation operators and another based on risk measuresallowing 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.
Cite
@article{arxiv.2501.14565,
title = {Higher-Order Stochastic Dominance Constraints in Optimization},
author = {Rajmadan Lakshmanan and Alois Pichler and Miloš Kopa},
journal= {arXiv preprint arXiv:2501.14565},
year = {2025}
}