聚合风险模型下指数保费的非参数估计  

The Nonparametric Estimate of Exponential Premium Under Collective Risk Models

作　　者：张林娜[1] 温利民[1,2] 方婧[1] 

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：《西南大学学报（自然科学版）》2016年第5期100-105,共6页Journal of Southwest University(Natural Science Edition)

基　　金：国家自然科学基金项目(71361015);教育部人文社科基金项目(15YJC910010);中国博士后科学基金项目(2013M540534);江西省研究生创新基金项目(YC2014-S162)

摘　　要：在聚合风险模型的假设下,研究了聚合风险下指数保费的非参数估计,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收敛速度及渐近正态性.The exponential premium principle is one of the most important premium principles and is wide- ly applied in non-life insurance actuarial science. In this paper, the nonparametric estimate of exponential premium is investigated under collective risk models. In addition, the estimator is proved strongly consist- ent and asymptotically normal. Finally, a numerical simulation method is used to verify the estimated speed of convergence, and the asymptotic normality of the estimator is checked in the simulations.

关 键 词：聚合风险模型 指数保费 非参数估计 相合性 渐近正态性 

分 类 号：O211.5[理学—概率论与数理统计]