两险种广义Erlang(2)风险模型的破产概率  

On the Ruin Probability for a Generalized Erlang(2) Risk Model Involving Two Classes of Insurance Risks

作　　者：王后春[1] 

机构地区：[1]安徽建筑大学数理系,合肥230601

出　　处：《工程数学学报》2013年第5期661-672,共12页Chinese Journal of Engineering Mathematics

基　　金：安徽高校省级自然科学研究项目(KJ2012Z050;KJ2012A056)~~

摘　　要：本文考虑一类具有两个独立险种的风险模型的破产概率,假设该模型的两个索赔计数过程是独立的两个广义Erlang(2)过程.利用微分分析和矩阵表示,得到破产概率满足的一个积分–微分方程组及其边界条件.在索赔计数过程是普通Erlang(2)过程的情形下,证明了广义Lundberg方程有且仅有三个正的实数根,由此并结合破产概率满足的积分–微分方程组,给出了破产概率的Laplace变换.In this paper, we consider the ruin probability for a risk model involving two inde- pendent classes of insurance risks. It is assumed that the claim number processes in this model are two independent generalized Erlang（2） processes. Firstly, a system of integro-differential equations with boundary conditions for the ruin probability is derived by differential analysis and matrix representation. Secondly, in the case where the claim number processes are two independent ordinary Erlang（2） processes, we discuss the generalized Lundberg equation and show that the equation has exactly three positive real roots which play an important role. Finally, the Laplace transform of the ruin probability is obtained in the same case.

关 键 词：两险种风险模型 广义Erlang（2）过程 破产概率 积分-微分方程 LAPLACE变换 

分 类 号：O211.9[理学—概率论与数理统计]