带多级免赔额的风险保费及其贝叶斯估计  

The Risk Premiums and Its Bayesian Estimates with Multi-Level Deductibles

作　　者：温利民[1,2] 周景萃 刘志强[1] 刘蔚 WEN Limin;ZHOU Jingcui;LIU Zhiqiang;LIU Wei(School of Mathematics and Statistics,Jiangxi Normal University,Nanchang Jiangxi 330022,China;Jiangxi Applied Mathematics Center,Jiangxi Normal University,Nanchang Jiangxi 330022,China)

机构地区：[1]江西师范大学数学与统计学院,江西南昌330022 [2]江西师范大学江西应用数学中心,江西南昌330022

出　　处：《江西师范大学学报（自然科学版）》2024年第3期260-268,共9页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金(72263019);江西省教育厅基金(GJJ200308);江西省自然科学基金(20224BCD41001)资助项目。

摘　　要：在汽车保险中,保单设计常常会提供多个级别的免赔额以供被保险人选择.因此,在汽车保险的聚合风险模型中,将索赔额按大小分为若干级别.进而,建立了在均值-方差保费原理下风险保费的贝叶斯模型,并获得了风险保费和贝叶斯估计的显式解.研究结论显示:在一定条件下,贝叶斯估计能表达为样本估计和聚合估计的加权平均.同时,研究了风险保费的线性贝叶斯估计,获得了在任意分布下风险保费的最优信度估计,证明了贝叶斯估计和信度估计的强相合性和渐近正态性.最后,利用数值模拟方法验证了估计的大样本性质.In car insurance,there are often multiple levels of deductibles for the insured to choose from in the policy design.Therefore,in the aggregate risk model of car insurance,the claim amounts are divided into several levels,and under the mean-variance premium principle,the Bayesian estimation of risk premiums is studied.The conclusion shows that under certain conditions,Bayesian estimation can be expressed as a weighted average of sample estimation and aggregate estimation.Furthermore,the credibility estimation of risk premiums is studied,and the strong consistency and asymptotic normality of Bayesian estimation and credibility estimation are also proved.Finally,the properties of the estimation are verified using numerical simulation methods.

关 键 词：聚合风险模型 风险保费 多级免赔额 信度估计 渐近正态性. 

分 类 号：O212.2[理学—概率论与数理统计]