Distortion risk measures in portfolio optimization

The paper deals with mean-risk problems where the risk is modeled by a distortion measure. This measure could be seen as a generalization of Conditional Value-at-Risk or Expected shortfall. If the associated distortion function is concave the measure is coherent. We analyze several distortion measures for different choices of a concave distortion function. First, assuming a discrete distribution of returns, we identify the efficient frontier. Then we compute the portfolio maximizing reward-risk ratio. Finally, we compare the results for various distortion measures among each other.