复合Poisson-Geometric风险模型Gerber-Shiu折现惩罚函数  

The Geber-Shiu Discounted Penalty Function in with Poisson-Geometric Risk Model

作　　者：廖基定[1] 龚日朝[2] 刘再明[1] 邹捷中[1] 

机构地区：[1]中南大学数学与计算技术学院 [2]湖南科技大学商学院,湘潭411201

出　　处：《应用数学学报》2007年第6期1076-1085,共10页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10371133);教育部人文社会科学规划基金项目-我国巨灾管理体系与保险机制建设研究(07JA790084);湖南省社科基金(06YB63);湖南省教育厅优秀青年基金(06B34);湖南省教育厅科研项目(06C715)资助项目.

摘　　要：本文研究赔付为复合Poisson-Geometric过程的风险模型,首先得到了Gerber-Shiu折现惩罚期望函数所满足的更新方程,然后在此基础上推导出了破产概率和破产即刻前赢余分布等所满足的更新方程,再运用Laplace方法得出了破产概率的Pollazek-Khinchin公式,最后根据Pollazek-Khinchin公式,直接得出了当索赔分布服从指数分布的情形下破产概率的显示表达式.In the paper the Gerber-Shiu discounted penalty function has been studied in risk model, which the claim process is a compound Poisson-Geometric process and the defective renewal equation of the Gerber-Shiu discounted penalty function has been given. Through the above result the defective renewal equation about the ruin probability and the marginal distributions of the deficit at ruin have been deduced. Finally the Pollazek-Khinchin formula of ruin probability has been obtained using Laplace transform method and based on the Pollazek-Khinchin formula the express of ruin probability has been obtained when the claim variable random belongs to the exponential distribution.

关 键 词：复合POISSON-GEOMETRIC过程 风险模型 破产概率 Pollazek-Khinchin公式 

分 类 号：O211.67[理学—概率论与数理统计]