Portfolio Optimization with Higher Moment Risk Measures

The paper considers modeling of risk-averse preferences in stochastic programming problems using risk measures. We utilize the axiomatic foundation of coherent risk measures and deviation measures in order to develop simple representations that express risk measures via solutions of specially constructed stochastic programming problems. Using the developed representations, we introduce a new family of higher-moment coherent risk measures (HMCR), and, in particular, the second-moment coherent risk measure (SMCR). It is demonstrated that the HMCR measures are compatible with the second order stochastic dominance, and can be efficiently used in portfolio optimization