OPTIMIZATION WITH MULTIVARIATE STOCHASTIC DOMINANCE CONSTRAINTS

We consider risk-averse stochastic optimization problems with a risk-shaping constraint in the form of a multivariate stochastic order constraint. The constraint requires that a random vector depending on our decisions stochastically dominates a given benchmark random vector in the sense of the linear stochastic dominance of second order. We refine the optimality conditions for problems with this type of constraint by using atomic measures. Additionally, we propose a primal and a dual numerical method for solving the problem and formulate sufficient conditions for their convergence. Numerical experience and comparisons to other approaches are provided.