带干扰的Sparre-Andersen对偶风险模型  

On the Sparre-Andersen dual model perturbed by diffusion

作　　者：陈昱[1] 张棋 CHEN Yu;ZHANG Qi(Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei 230026, China)

机构地区：[1]中国科学技术大学管理学院统计与金融系,合肥230026

出　　处：《中国科学技术大学学报》2019年第9期689-698,共10页JUSTC

基　　金：the National Key Research and Development Plan(2016YFC0800104);the National Natural Science Foundation of China(71771203).

摘　　要：研究了带干扰的对偶风险模型,其中收入时间间隔是服从于广义Erlang(n)分布的独立同分布的随机变量.推导出了破产时间Laplace变换满足的积分-微分方程和边界条件,并且得到了其精确表表达式.特别地,以收入变量服从指数分布为例,给出了破产时间Laplace变换的具体解.最后,考虑了阈值分红下的带干扰的对偶风险模型,得到了期望折现分红满足的积分-微分方程和边界条件.A diffusion perturbed Sparre-Andersen dual risk model was studied,in which the times between gains are independent and identically distributed random variables with a generalized Erlang(n)distribution.An integro-differential equation with certain boundary for the Laplace transform of the ruin time was derived and then its explicit expression was obtained.In particular,an explicit form of the Laplace transform of the time to ruin were studied when jump sizes were exponential.Finally,by studying the expected discounted dividends with the threshold-dividend strategy in the diffusion perturbed Sparre-Andersen dual risk model,an integro-differential equation with certain boundary for the expected discounted dividends was derived.

关 键 词：Sparre-Andersen对偶模型 广义Erlang(n)更新时间 破产时间 折现分红支付 

分 类 号：O211.67[理学—概率论与数理统计]