Optimization with Stochastic Dominance Constraints

Preference between random variables is frequently expressed by comparing their distributions via a stochastic order. A variety of stochastic-order relations exist (also called stochastic orderings), which express preferences among univariate random outcomes, random vectors, sequences, or processes. A large body of literature is dedicated to their properties and relations among them. We focus on the most popular orders, which are suitable to model risk-averse preferences. The presentation of their properties is limited to those that are relevant to the analysis and numerical solution of the related stochastic optimization problems.