Multistage portfolio optimization with multivariate dominance constraints

In this article we focus on multistage portfolio optimization problem with usage of multivariate stochastic dominance constraints. The first part of the work is devoted to the theoretical background needed for establishing the optimization problem. We provide a general approach to multivariate stochastic dominance, we mainly recall basic definitions and several statements that are relevant for portfolio optimization, and describe an algorithm for detecting multivariate stochastic dominance of two random vectors with discrete distributions. The main part of the work introduces multivariate stochastic dominance constraints in multistage portfolio optimization problem. We compare obtained results with traditional model which employs univariate first order stochastic dominance constraints at each stage.