带投资和债务利率的Sparre Andersen风险模型(英文)  

The Sparre Andersen Risk Process with Investment and Debit Interest

作　　者：赵永霞[1,2] 

机构地区：[1]华东师范大学金融与统计学院,上海200241 [2]曲阜师范大学数学科学学院,曲阜273165

出　　处：《应用概率统计》2013年第5期495-514,共20页Chinese Journal of Applied Probability and Statistics

基　　金：supported by National Natural Science Foundation of China(11231005,11226251);Doctoral Program Foundation of the Ministry of Education of China(20110076110004);"the Fundamental Research Funds for the Central Universities"

摘　　要：这篇文章,研究了带投资和债务利率的Sparre Andersen风险模型的绝对破产问题.首先,得到了在绝对破产时折扣罚金函数满足的带边界值的积分–微分方程.然后,得到了绝对破产时折扣罚金函数满足的更新方程,进而分别在索赔额是轻尾和重尾时,得到了折扣罚金函数两个的渐进结果.最后,在索赔间隔服从广义Erlang(2)分布和索赔额服从指数分布的情况下,得到了具体的表达式和一些数值结果.In this paper, we study absolute ruin problems for the Sparre Andersen risk process with generalized Erlang（n）-distributed inter-claim times, investment and debit interest. We first give a system of integro-differential equations with certain boundary conditions satisfied by the expected discounted penalty function at absolute ruin. Second, we obtain a defective renewal equation under some special cases, then based on the defective renewal equation we derive two asymptotic results for the expected discounted penalty function when the initial surplus tends to infinity for the light- tailed claims and heavy-tailed claims, respectively. Finally, we investigate some explicit solutions and numerical results for generalized Erlang（2） inter-claim times and exponential claims.

关 键 词：绝对破产 利率 折扣罚金函数 渐进 

分 类 号：O211.67[理学—概率论与数理统计]