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

Abstract

In this paper, we present an efficient scenario reduction method for optimization problems whose objective function is the higher moment coherent risk (HMCR) measures. Compared with existing approaches, our method places greater emphasis on the characteristics of optimization problems. Because the value of HMCR measures only depends on a small subset of scenarios that correspond to high cost or loss, our approach is based mostly on the concept of ineffective scenarios previously proposed in the literature, which entails identifying the scenarios whose removal from the problem results in no change of the optimal value. We test our method on a simple portfolio optimization problem with only nine risky assets and a realistic one with 50 risky assets and cardinality constraints. Results show that our scenario reduction method can yield a more accurate optimal solution and optimal value, along with a smaller reduced-scenario set. Even at the same reduction level, our method continues to outperform the existing scenario reduction methods. Interestingly, the portfolio produced by our method is also more diversified than others. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by the National Natural Science Foundation of China [Grants 71720107002 and U1901223]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0375 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0375 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .