对损失规律的一种新解释：混合负二项分布及其应用

一、引言在世界上任何一个国家 ,几乎所有的汽车保险人都采用了无赔款优待系统 ,即所谓的ＢＭＳ(Ｂｏｎｕｓ ＭａｌｕｓＳｙｓｔｅｍ)。在该系统中 ,保险公司将根据投保人以往年份的索赔情况调整其续期保费。通常的原则是 ,上一保险年度发生的索赔次数越多 ,次年的续期保费将越高。反之 ,如果上一保险年度没有发生索赔 ,保险公司将降低投保人的续期保费。毫无疑问 ,保险公司调整投保人续期保费的主要目的之一就是为了公平投保人的保费负担 ,使高风险的投保人缴纳相对较高的保险费。但是 ,实证研究结果表明 (参见文献 1]) ,保险公司目前应用…

A new explanation of Loss Regularity--the mixed negative binomial distribution and its utility

Because of some practical reasons, we suppose that the claim number of a given policy holder is a negative binominal distribution and the structure function of the portfolio is a Beta distribution, then we get a mixed negative binominal distribution(i.e. negative binominal-Beta distribution). The paper discuss the property of the mixed negative binominal distribution and its application to a set of practical data from insurance practice. The result shows that the mixed negative binominal distribution can fit the real observation of claim numbers very well. So we use this model to construct the optimal BMS to adjust the renewal premium of the policy holders. Compared with other BMS’s, this one is more feasible in practice.