具有随机支出的带延迟的对偶保险风险模型  

The Delayed Dual Risk Model with Stochastic Expense

作　　者：周纹心 申海燕 周国立[2] ZHOU Wenxin;SHEN Haiyan;ZHOU Guoli(School of Economics and Management,Chongqing Normal University,Chongqing 401331,China;School of Mathematics and Statistics,Chongqing University,Chongqing 401331,China)

机构地区：[1]重庆师范大学经济与管理学院,重庆401331 [2]重庆大学数学与统计学院,重庆401331

出　　处：《江西师范大学学报（自然科学版）》2021年第4期343-348,共6页Journal of Jiangxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金面上课题(11971077);重庆市自然科学基金(cstc2020jcyj-msxm2554)资助项目。

摘　　要：该文考虑了在带延迟的对偶风险模型中支出服从指数分布的情况.首先,运用无穷小分析法以及随机过程的基本理论推导出破产时间的拉普拉斯变换、破产概率和破产时间的期望所满足的积分-微分方程;其次,运用常微分方程方法得到了当随机支出和收入变量均为指数分布时的破产概率和相关破产时间的解析表达式;最后,列举了数值实例来论证在模型中的某些参数对破产概率的影响.The case that expense follows exponential distribution in the delayed dual risk model is considered.Firstly,by using the infinitesimal method and the basic theory of stochastic processes,the integral equations of the Laplace transform of the ruin time,the ruin probability and the expected value of the ruin time are derived.Secondly,when the stochastic expense and revenue variables are exponential distribution,the explicit expressions for ruin probability and related ruin time by using the ordinary differential equation are obtained.Finally,numerical examples are given to demonstratethe effect of some parameters in this model on ruin probability.

关 键 词：对偶风险模型 延迟 随机支出 积分方程 指数分布 

分 类 号：O211.67[理学—概率论与数理统计]