English

Higher-Order Stochastic Dominance Constraints in Optimization

Optimization and Control 2025-02-27 v3

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\unicodex2013\unicode{x2013}one employs expectation operators and another based on risk measures\unicodex2013\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.

Keywords

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}
}
R2 v1 2026-06-28T21:16:22.040Z