Cut generation for optimization problems with multivariate risk constraints

We consider a class of multicriteria stochastic optimization problems that features benchmarking constraints based on conditional value-at-risk and second-order stochastic dominance. We develop alternative mixedinteger programming formulations and solution methods for cut generation problems arising in optimization under such multivariate risk constraints. We give the complete linear description of two non-convex substructures appearing in these cut generation problems. We present computational results that show the effectiveness of our proposed models and methods.