均值-方差模型中保费的最优分配及其统计分析  

Optimal Allocation and Statistical Analysis of Premiums in Mean-Variance Models

作　　者：温利民[1] 崔梦琪 章溢 Wen Limin;Cui Mengqi;Zhang Yi(School of Mathematics and Statistics,Jiangxi Normal University,Nanchang 330022,China;School of Finance,Jiangxi Normal University,Nanchang 330022,China)

机构地区：[1]江西师范大学数学与统计学院,南昌330022 [2]江西师范大学财政金融学院,南昌330022

出　　处：《统计与决策》2024年第20期55-60,共6页Statistics & Decision

基　　金：国家自然科学基金地区项目(72263019);江西省高校人文社会科学研究规划项目(TJ22202);江西省自然科学基金资助项目(20242BAB25017);赣鄱俊才支持计划-文化领军人才培养项目(2023)

摘　　要：在保险实务中,保险公司需要将保单组合的总保费分配在各个保单中,以使得保费与风险尽可能匹配。文章提出了改进的均值-方差保费分配模型,得到了最优保费分配的显式解。结果表明,不论是均值模型还是改进的均值-方差模型,每个风险上的最优保费分配恰为该风险上的保费与差额保费的加权平均。进而,给出了保费分配的最优解的非参数估计,并证明了估计的大样本性质。最后,利用已有文献的数据,给出了改进的均值-方差模型的最优保费分配解,并验证了最优解估计的收敛性。In insurance practice,insurance companies need to allocate the total premiums of the policy portfolio among individual policies,so that the premiums match the risks as much as possible.This paper proposes an improved mean-variance premium allocation model,and obtains the explicit solution of the optimal premium allocation.The results show that regardless of the mean model or the improved mean-variance model,the optimal premium allocation on each risk is just the weighted average of the premium and the difference premium on that risk.Furthermore,a nonparametric estimate of the optimal solution for premium allocation is given,and the large sample properties of the estimation are proved.Finally,based on the data of existing literature,the optimal solutions of premium allocation of the improved mean-variance model are given,and the convergence of the optimal solution estimation is verified.

关 键 词：保费分配 均值-方差模型 非参数估计 相合性 渐近正态性 

分 类 号：O211.9[理学—概率论与数理统计]