两险种广义复合Poisson模型资金下降到初始盈余的贴现罚金函数  

Discounted penalty function of generalized compound Poisson model of two type insurence when funds fall to initial surplus

作　　者：李婧彬 王秀莲[1] 邹华 LI Jingbin;WANG Xiulian;ZOU Hua(College of Mathematical Science,Tianjin Normal University,Tianjin 300387,China)

机构地区：[1]天津师范大学数学科学学院

出　　处：《天津师范大学学报（自然科学版）》2019年第6期7-11,共5页Journal of Tianjin Normal University：Natural Science Edition

基　　金：天津市高等学校科技发展计划资助项目（JW1714）

摘　　要：考虑两险种广义复合Poisson模型,研究当资金下降到初始盈余时关于停时的贴现罚金函数.利用概率论方法及Laplace变换,推导出该模型贴现罚金函数满足的积分微分方程以及更新方程,进一步得出贴现罚金函数的具体表达式和资金下降到初始盈余时停时的矩,并对索赔额服从指数分布的情况给出了贴现罚金函数的显式表达式.The generalized compound Poisson model of two type insurence is considered. The discounted penalty function about the stopping time when funds fall to initial surplus is studied. The integral differential equation and renewal equation for the discounted penalty function is deduced by using probability theory and the Laplace transform,and then the concrete expression of the discounted penalty function and the moment of stopping time are obtained. The explicit expression of the discounted penalty function is given when the claim amount distribution is the exponential.

关 键 词：贴现罚金函数 广义复合Poisson模型 积分微分方程 LAPLACE变换 矩 

分 类 号：O211.67[理学—概率论与数理统计]