Stochastic Dominance Constrained Portfolio Optimization with Distortion Risk Measures

The paper deals with risk-minimizing, stochastic dominance constrained portfolio optimization problems where the risk is modeled by distortion measures. These measures could be seen as a generalization of Value at Risk, Conditional Value at Risk or Expected shortfall. If the associated distortion function is concave the measure is coherent. We analyze several such portfolio selection problems for different choices of a concave distortion function. First, assuming a discrete distribution of returns, we identify in sample optimal portfolios with and without second order stochastic dominance constraints. Then we compute the out-of-sample characteristics. Finally, we compare the in sample and out-of-sample results of all considered models among each other.