基于两个独立的指数随机变量之和的相依风险模型的破产问题研究  

Research on the Ruin Problem of Dependent Risk Model Based on the Sum of Two Independent Exponential Random Variables

作　　者：王婧璇 

机构地区：[1]辽宁师范大学数学学院,辽宁 大连

出　　处：《应用数学进展》2023年第7期3447-3462,共16页Advances in Applied Mathematics

摘　　要：在本文中我们考虑了经典复合泊松模型的一个推广,该模型的累计索赔额过程的增量是独立的。其中索赔间隔时间的分布是两个独立的指数随机变量之和,在本文中我们考虑了索赔时间与后续索赔规模之间的一种特殊的依赖结构,导出了Gerber-Shiu惩罚函数的积分微分方程,利用Rouché定理研究了林德伯格等式的根,导出了惩罚函数的拉普拉斯变换及其满足的瑕疵更新方程。最后在索赔时间间隔服从两个独立的指数随机变量之和分布时给出破产概率的解析解,对理论结果做数值分析,对不同相依参数下的破产概率进行对比。In this paper, we consider an extension of the classical compound Poisson model where the incre-mental cumulative claims process is independent. The distribution of claim interval follows the sum of two independent random variables. In this paper, we consider a special dependence structure between claim time and subsequent claim scale, derive the Gerber-Shiu penalty function integral differential equation, and use Rouché’s theorem to study the roots of Lundberg equation. The La-place transform of penalty function and its defect renewal equation are derived. Finally, the analytic solution of ruin probability is given when the claim interval follows the sum distribution of two in-dependent exponential random variables. The theoretical results are analyzed numerically, the ru-in probabilities under different dependent parameters are compared.

关 键 词：两个独立的指数随机变量之和分布 积分微分方程 林德伯格等式 Gerber-Shiu期望贴现惩罚函数 拉普拉斯变换 瑕疵更新方程 

分 类 号：G63[文化科学—教育学]