非时齐复合泊松过程下对偶风险模型的破产特征量研究  

Analysis on Ruin-related Quantities of Dual Risk Model under Nonhomogeneous Compound Poisson Process

作　　者：胡康 韩恒秀 李满 邓迎春 HU Kang;HAN Hengxiu;LI Man;DENG Yingchun(School of Mathematics and Statistics,Hunan Normal University,Changsha 410081,China)

机构地区：[1]湖南师范大学数学与统计学院,湖南长沙410081

出　　处：《经济数学》2020年第1期84-91,共8页Journal of Quantitative Economics

基　　金：湖南省哲学社会科学基金资助项目(17YBA290);湖南省教育厅科学研究资助项目(17K057)。

摘　　要：将经典的对偶风险模型中的收益到达过程推广为非时齐的泊松过程.运用经典方法和时变方法,计算了该模型下的破产概率,并定义了时变后相应模型的广义期望折罚函数,验证了时变方法对非时齐泊松风险模型的有效性,最后又考虑了该模型在带壁分红策略下的情形,当单次索赔额服从指数分布时,得到了它的期望折罚函数以及期望折现分红函数.The income arrival process of classical dual risk model is extended to nonhomogeneous compound Poisson risk model,both the classical method and the time-varying method are used to calculate the ruin-related quantities in this model,and the analytical expression of the renewal equation is obtained.For the time-varying model,a generalized expected discounted penalty function is defined to verify the effectiveness of the time-varying method to the nonhomogeneous compound Poisson risk model.The dual risk model with barrier dividend is considered,the expected discounted penalty function and the expected dividend function of the model are obtained when the single claim amount follows the exponentially distribution.

关 键 词：破产概率 非时齐泊松过程 时变方法 期望折罚函数 期望折现分红函数 

分 类 号：O211.67[理学—概率论与数理统计]