LIU Zhaomeng,HAN Youpan.Quantitative statistical robustness of conditional value at risk with moment-based uncertainty set[J].Journal of Yanbian University,2024,(02):54-59.
基于矩信息的不确定集下CVaR的定量统计稳健性
- Title:
- Quantitative statistical robustness of conditional value at risk with moment-based uncertainty set
- 文章编号:
- 1004-4353（2024）02-0054-06
- Keywords:
- robust risk measure; uncertainty set; quantitative statistical robustness ; conditional value at risk
- 分类号:
- O221.5
- 文献标志码:
- A
- 摘要:
- 研究了在最坏情况下CVaR的定量统计稳健性.首先，推导出了CVaR关于随机向量是Lipschitz的；其次，证明了在Kantorovich度量下，分布不确定集在某一确定点附近是局部Lipschitz的，由此得出分布式鲁棒CVaR模型的最优值函数满足Lipschitz连续性；最后，在最坏情况下推导出了CVaR的定量统计稳健性.
- Abstract:
- The quantitative statistical robustness of conditional value at risk (CVaR) in the worst-case is studied. Firstly， CVaR is Lipschitz with random vectors. Secondly，the distribution uncertainty set is locally Lipschitz near a certain point under the Kantorovich metric，thereby the optimal value function of the distributed robust CVaR model satisfies Lipschitz continuity. Finally，the quantitative statistical robustness of the worst-case CVaR is derived.
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备注/Memo
投稿日期：2024-04-12
基金项目：国家自然科学基金（11501434）；陕西省自然科学基金（2023-JC-YB-063）
第一作者：刘兆萌（1999—），女，硕士研究生，研究方向为金融优化和最优化理论.
通信作者：韩有攀（1980—），男，博士，副教授，研究方向为金融优化、集值优化和传统优化理论.