An Efficient Scenario Reduction Method for Problems with Higher Moment Coherent Risk Measures.

This article focuses on developing an efficient scenario reduction method for stochastic optimization problems that minimize higher moment coherent risk (HMCR) measures, a class of tail risk measures extending conditional value-at-risk (CVaR) by incorporating higher moments of loss distributions. The method leverages the concept of ineffective scenarios—scenarios whose removal does not affect the optimal value—to reduce the scenario set while preserving solution accuracy. Theoretical results characterize ineffective scenarios for HMCR-based problems, and an approximate reduction algorithm is proposed using existing scenario reduction techniques to estimate the optimal solution. Empirical tests on portfolio optimization problems with nine and 50 risky assets demonstrate that the proposed method outperforms existing approaches in terms of objective value accuracy, investment decision error, reduced scenario set size, and portfolio diversification, especially when the moment order exceeds one.