聚合风险模型下Esscher风险度量的估计及其大样本性质  

The Estimate and Its Large Sample Properties of for Esscher Risk Measure Under Collective Risk Models

作　　者：温利民[1,2] 方婧[1] 梅国平[1,2] 

机构地区：[1]江西师范大学数学与信息科学学院,南昌330022 [2]江西财经大学信息管理学院,南昌330013

出　　处：《应用数学学报》2015年第2期330-339,共10页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(71361015;71340010);江西省自然科学基金(20142BAB201013);中国博士后特别资助项目(2014T70615);中国博士后面上项目(2013M540534);江西省博士后择优项目(2013KY53)资助

摘　　要：Esscher度量是一种重要的风险度量,在金融风险管理、保险精算中有广泛的应用,然而大部分关于Esscher风险度量的文献均在个体风险模型下考虑的.本文建立了聚合风险模型下Esscher度量的估计模型,得到了相应的非参数估计,并证明了估计的强相合性和渐近正态性,最后,通过数值模拟的方法验证了估计的大样本性质.Esscher measure is an important risk measure which is widely used in financial risk management, statistics and actuarial science. However, most of the literature on Esscher risk measure are considered only in individual risk models. In this paper, the estimate mod- els of Esscher measure under the collective risk are built and corresponding non-parametric estimation of Esscher measure are derived. In addition, the strong consistency and asymp- totic normality are proved. Finally, the numerical simulation methods are given to verify the large sample properties of the estimator.

关 键 词：Esscher风险度量 估计 相合性 渐近正态性 

分 类 号：O212.7[理学—概率论与数理统计]