统计与决策2024，Vol.40Issue(9)：55-60,6.DOI:10.13546/j.cnki.tjyjc.2024.09.009
基于分数阶矩和分片Wasserstein距离的鲁棒风险度量优化模型
Robust Risk Measurement Optimization Model Based on Fractional Moment and Piecewise Wasserstein Metric
摘要
Abstract
Robust risk measurement optimization is a class of important issue in the stochastic risk measurement.The cap-ture of uncertain distribution information depends on imperfect assumptions and estimates,and the reflection of the tail of distribu-tion directly affects the accuracy of distribution prediction.The error of the tail model can cause serious consequences in actual risk management decision-making.This paper constructs a robust risk measurement optimization model in a way that is robust to the error of the tail model.In the case of constructing the model uncertainty set,a distribution estimation method based on Wasser-stein metric is proposed to overcome the limitation that the existing parameter distributions cannot reflect the real distribution tail behavior.In view of the ability of fractional moment to accurately describe the tail information of distribution,a robust risk mea-surement model with fractional moment constraints is established based on the analysis of distribution estimation.Furthermore,a piecewise robust risk measurement model with piecewise Wasserstein metric constraints is constructed based on fiber bundles the-ory to optimize the tail model error caused by the fact that Wasserstein metric ignores the distribution geometry.Finally,the simu-lation analysis of normative data is performed,and the results show that the model can accurately quantify the risk of sudden ex-treme loss.关键词
鲁棒风险度量/分数阶矩/概率分布估计/分片Wasserstein距离Key words
robust risk measurement/fractional moment/probability distribution estimation/piecewise Wasserstein metric分类
数理科学引用本文复制引用
李伟梅,高雷阜..基于分数阶矩和分片Wasserstein距离的鲁棒风险度量优化模型[J].统计与决策,2024,40(9):55-60,6.基金项目
国家自然科学基金资助项目(12201275) （12201275）
教育部人文社会科学研究基金项目(21YJCZH204) （21YJCZH204）
辽宁省社会科学规划基金项目(L22BGL028) （L22BGL028）
