基于WOD序列风险度量VaR和CVaR估计的渐近性质  

Asymptotic Properties of VaR and CVaR Estimators for Widely Orthant Dependent Samples

作　　者：李永明[1] 罗中德[2] 李乃医 邢国东 LI YONGMING;LUO ZHONGDE;LI NAIYI;XING GUODONG(School of Mathematics and Computational Science,Shangrao Normal University,Shangrao 334001,China;School of Mathematics,Physics and Statistics,Baise University,Baise 533000,China;School of Mathematics and Computer,Guangdong Ocean University,Zhanjiang 524088,China;School of Mathematics and Statistics,Hefei Normal University,Hefei 230061,China)

机构地区：[1]上饶师范学院数学与计算科学学院,上饶334001 [2]百色学院数理科学与统计学院,百色533000 [3]广东海洋大学数学与计算机学院,湛江524088 [4]合肥师范学院数学与统计学院,合肥230061

出　　处：《应用数学学报》2024年第3期478-497,共20页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金项目(批准号:12161075);江西省自然科学基金重点项目(批准号:20212ACB201006);广东省自然科学基金项目(批准号:2022A1515010978,2024A1515011258);安徽高校自然科学基金(批准号:KJ2020A0122)资助项目。

摘　　要：在WOD序列下分别考虑了风险价值VaR和条件风险价值CVaR的估计.研究了VaR样本分位数估计的Bahadur表示以及强相合性.同时,对条件风险价值CVaR估计的强相合性及其收敛速度进行研究,通过选取适当的参数其收敛速度接近于O(n-1/2).为了说明所得的VaR和CVaR估计的理论结果,我们分别利用ARMA(1,1)模型和MA(1)模型产生的WOD随机数进行了数值模拟,通过VaR和CVaR相应的真实值和估计值曲线图对理论结果的有效性进行了验证.Under widely orthant dependent samples,two kinds of risk measure are considered.The Bahadur representation and strong consistency of the quantile estimator for VaR are discussed.And the strong consistency and its rate of the CVaR estimator are established,by the suitable choice of some constants,their rates are near O(n-).In order to better illustrate performances of the VaR and CVaR estimators,we conduct numerical simulations under some WOD sequences by ARMA(1,1)and MA(1)models,and discover that the estimators are high performance by tables of the exact and estimated values of VaR and CVaR,and their curve figures.

关 键 词：WOD相依 风险价值 条件风险价值 BAHADUR表示 强相合性 

分 类 号：O212.7[理学—概率论与数理统计]