方差相关原理下相依聚合风险模型的贝叶斯保费

华东师范大学学报(自然科学版) ›› 2014, Vol. 2014 ›› Issue (4): 26-38.

方差相关原理下相依聚合风险模型的贝叶斯保费

余君¹, 温利民^1,2

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

收稿日期:2013-07-01 修回日期:2013-10-01 出版日期:2014-07-25 发布日期:2014-07-25

Bayes premium under variance-related principles with risk dependence

YU Jun¹, WEN Li-min^1,2

1. Institute of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China; 2. School of Information Management, Jiangxi University of Finance and Economics, Nanchang 330013, China

Received:2013-07-01 Revised:2013-10-01 Online:2014-07-25 Published:2014-07-25

摘要/Abstract

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.

关键词: 风险相依, 方差相关保费原理, 聚合保费, 贝叶斯保费

Abstract: 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 Sarmanov-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 are
highly sensitive even at the moderate levels of correlation between
the risk profiles.

Key words: risk dependence, variance-related premium principle, collective premium, Bayes premium

中图分类号:

O157.5

余君, 温利民. 方差相关原理下相依聚合风险模型的贝叶斯保费[J]. 华东师范大学学报(自然科学版), 2014, 2014(4): 26-38.

YU Jun, WEN Li-min. Bayes premium under variance-related principles with risk dependence[J]. Journal of East China Normal University(Natural Sc, 2014, 2014(4): 26-38.

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