二级保费率下Erlang(2)过程风险模型的分析  

The Analysis of the Erlang(2) Risk Model with a Two-step Premium Rate

作　　者：郭淑妹[1] 林涛[1] 

机构地区：[1]厦门大学数学科学学院,福建厦门361005

出　　处：《厦门大学学报（自然科学版）》2008年第5期644-646,共3页Journal of Xiamen University：Natural Science

摘　　要：随着国内保险业的逐步成熟和完善,保险业也要与世界接轨,分红险种也逐步进入中国保险市场.分红险种除了投保人在需要理赔时获得应有的理赔外,还应向投保人支付红利,使得投保人获得类似与于股票一样的收益,因此对支付红利问题的研究显得十分必要和有意义.本文研究了二级保费率下即具有常量红利界限的Erlang(2)过程风险模型的折现函数.通过对Gerber-Shiu折现函数的分析,采用微分方程特解与通解的关系及一些已有结论求解Gerber-Shiu折现函数及与破产有关的问题.With the gradually maturation and improvement of insurance industry in China,the dividends insurance entered Chinas insurance market gradually. The policyholder receives not only the compensation which the dividends insurance claims in need, but also the dividend like stock, So the research of payment of dividend is necessary and meaningful. The Gerber-Shiu discounted penalty function of a Erlang（2） risk model with a two-step premium rate that the boundaries of a constant dividend was studied in this paper. By the analysis of the Gerber-Shiu discounted penalty function, the expressions of Gerber-Shiu discounted penalty function and some correlative problems were obtained by using the especial result and common result of the integro-differential equation and some known result.

关 键 词：Gerber-Shiu折现函数 二级保费 微分方程 ERLANG(2)风险过程 

分 类 号：O211[理学—概率论与数理统计]