带相依结构和常值红利界限风险模型的Gerber-Shiu贴现惩罚函数  

The Gerber-Shiu Discounted Penalty Function for the Risk Model with Dependence Structure and a Constant Dividend Barrier

作　　者：郭红爽 

机构地区：[1]辽宁师范大学数学学院,辽宁 大连

出　　处：《理论数学》2024年第5期60-68,共9页Pure Mathematics

摘　　要：我们考虑的是带相依结构和常值红利界限的复合泊松风险模型,其中索赔时间和索赔额服从某种二元分布。我们可以导出Gerber-Shiu贴现惩罚函数的微积分方程,我们还求解了该微积分方程,证明其解是无界限条件下的Gerber-Shiu函数和相关齐次微积分线性方程解的组合。We consider a compound Poisson risk model with dependence and a constant dividend barrier, where the claim amount and the interclaim time follow some bivariate distribution. An integrodifferential equation for the Gerber-Shiu discounted penalty function is derived. We also solve the integrodifferential equation and show that the solution is a linear combination of the Gerber-Shiu function with no barrier and the solution of an associated homogeneous integrodifferential equation.

关 键 词：Gerber-Shiu贴现惩罚函数 常值红利界限 破产理论 

分 类 号：O17[理学—数学]