离散时间状态下基于个体数据的RBNS准备金评估（英文）  

Individual RBNS Loss Reserving in Discrete Time Model

作　　者：黄金龙[1] 吴贤毅[1] 

机构地区：[1]华东师范大学统计与精算学系,上海200241

出　　处：《应用概率统计》2015年第3期289-308,共20页Chinese Journal of Applied Probability and Statistics

基　　金：supported by National Natural Science Foundation of China(71371074);Shanghai Philosophy and Social Science Foundation(2010BJB004)

摘　　要：本文研究了在离散时间状态下的一类RBNS准备金评估问题.基于个体数据的RBNS准备金是用未知参数的估计来取代RBNS负债的条件期望中的相应的参数得到的.文中与结案延迟有关的参数是用极大似然估计的方法得到的,同时我们也研究了这些估计的渐近性质.RBNS未决负债的条件期望是用WatsonNadaraya估计得到的.同时,本文还研究了由链梯法得到的基于聚合数据的准备金的渐近性质.最后我们通过模拟说明了在有限样本情形下,基于个体数据的准备金与聚合数据下的准备金相比具有更小的MSE.In this paper, we investigate the RBNS reserving problem in a discrete time model. The individual RBNS reserving is evaluated with the unknown quantities in the RBNS reserve replaced by their estimates. The parameters related to the settlement delay are estimated using the method of maximum likelihood and the weak convergence of the estimates are studied. The conditional means in the RBNS reserve are estimated by the Watson-Nadaraya estimate. Moreover, the weak convergence of the aggregate RBNS reserving computed by the chain ladder algorithm are also studied. Simulation studies in finite sample case show that the individual method has smaller MSE compared to the the aggregate method.

关 键 词：个体数据的RBNS准备金 聚合数据的RBNS准备金 极大似然估计 Watson-Nadaraya估计 渐近正态性 

分 类 号：O212.1[理学—概率论与数理统计]