Higher-Order Stochastic Dominance Constraints in Optimization
研究了带高阶随机占优约束的优化问题，将约束缩减为至多可数的测试点，提出基于期望算子和风险度量的验证方法，并通过数值实验展示了其在投资组合优化中的效果。
Abstract 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.