Decision problems with stochastic dominance constraints

The paper deals with portfolio optimization problems with stochastic dominance constraints. In these problems, we try to find the optimal portfolio with respect to some objective function among all portfolios that dominate a given benchmark by a stochastic dominance relation. We consider two orders of stochastic dominance (the first and the second order stochastic dominance) and the mean return criterion. Moreover, we employ three risk measures (variance, Value at Risk and conditional Value at Risk) as the objectives. Hence we find 9 optimal portfolios that minimize risk under mean return or stochastic dominance constraints. We use 30 years long history data from US stock market. Moreover, we apply the cross-validation techniques and we compare the evolution of the optimal portfolios during the last 5 years.