Risk-averse portfolio optimization via stochastic dominance constraints

Abstract

We consider the problem of constructing a portfolio of finitely many assets whose return rates are described by a discrete joint distribution. We present a new approach to portfolio selection based on stochastic dominance. The portfolio return rate in the new model is required to stochastically dominate a random benchmark. We formulate optimality conditions and duality relations for these models and construct equivalent optimization models with utility functions. Two different formulations of the stochastic dominance constraint, primal and inverse, lead to two dual problems which involve von Neumann-Morgenstern utility functions for the primal formulation and rankdependent (or dual) utility functions for the inverse formulation. We also discuss the relations of our approach to value at risk and conditional value at risk. Numerical illustration is provided.