摘要
基于个体索赔模型对准备金的评估已成为准备金评估研究的重要内容.本文基于广义线性模型,对个体索赔额及索赔数目建立责任准备金模型,给出未决赔款责任准备金的期望及方差.进而,根据样本数据对未知参数求解极大似然估计,并讨论了估计的强相合性和渐近正态性.并得到责任准备金的估计及其预测均方误差.最后,通过数值模拟的方法将本文得到的估计与链梯法进行比较,结果显示我们的估计明显优于链梯法估计.
The individual claim reserving has become an important part of the reserve evaluation research. In this paper, we construct a claims reserve model regarding the indi- vidual claim amount and the number of claims based on the generalized linear model, and get the expectation and variance of outstanding claims reserve. The parameters related to the model are estimated using the maximum likelihood method based on the sample data. We also prove the strong consistency and asymptotic normality of the estimations. In addi- tion, the estimator of the RBNS claims reserve and the mean square error are listed. Finally, simulation studies show that the individual method which is based on the generalized linear model is obviously better than the chain ladder method.
作者
张林娜
温利民
王江峰
王伟
ZHANG LINNA WEN LIMIN WANG JIANGFENG WANG WEI(School of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China Department of Statistics, Zhejiang Gongshang University, Hongzhou 310018, China Department of Mathematics, Ning Bo University, Ningbo 315211, China)
出处
《应用数学学报》
CSCD
北大核心
2017年第4期573-593,共21页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金(71361015)
江西省自然科学基金重点项目(20171ACB21022)
江西省社科十二五规划项目(15WDZT10)
教育部人文社科基金(15YJC910010
14YJC630085)资助
关键词
RBNS
广义线性模型
个体索赔
极大似然估计
渐近正态性
RBNS
generalized linear model
individual claim
maximum likelihood estimation
asymptotically normal
