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 that involve von Neuman–Morgenstern utility functions for the primal formulation and rank dependent (or dual) utility functions for the inverse formulation. The utility functions play the roles of Lagrange multipliers associated with the dominance constraints. In this way our model provides a link between the expected utility theory and the rank dependent utility theory. We also compare our approach to models using value at risk and conditional value at risk constraints. A numerical example illustrates the new approach.