方差相关原理下相依聚合风险模型的贝叶斯保费  

Bayes premium under variance-related principles with risk dependence

作　　者：余君[1] 温利民[1,2] 

机构地区：[1]江西师范大学数信学院,南昌330022 [2]江西财经大学信息管理学院,南昌330013

出　　处：《华东师范大学学报（自然科学版）》2014年第4期26-38,共13页Journal of East China Normal University(Natural Science)

基　　金：国家自然科学基金(71361015;71001046);江西省教育厅基金(GJJ13217);中国博士后科学基金(2013M540534);江西省博士后择优基金(05ZR14046)

摘　　要：在经典的聚合风险模型中,常常假设索赔次数和索赔额是相互独立的,然而在实际保险业务中,索赔额和索赔次数常常呈现相依情形.本文通过引入Sarmanov-Lee相依分布族的概念,在索赔次数和索赔额呈现某种特定相依结构的条件下,研究了聚合风险模型下方差相关保费原理的聚合保费和贝叶斯保费,并通过数值模拟,对保费估计的稳健性进行了分析.结果表明,即使参数间的相依程度很小,也会对聚合风险保费和贝叶斯保费带来较大的影响.In a classical collective risk model, the claim numbers and claim amounts are usually assumed to be independent of each other, but in the actual business of insurance, they are generally dependent. In this paper, by introducing the concept of Saxmanov-Lee family of dependent distributions, the collective premium and Bayes premium were researched under variance-related the premium principle with the dependence between the risk profiles. Finally, the robustness of premium estimator were checked by numerical analysis. The results show that the collective premium and Bayes premium axe highly sensitive even at the moderate levels of correlation between the risk profiles.

关 键 词：风险相依 方差相关保费原理 聚合保费 贝叶斯保费 

分 类 号：O157.5[理学—数学]