常红利边界下带干扰的双复合Poisson风险模型  

Double compound Poisson risk model perturbed by diffusion with a constant dividend barrier

作　　者：赵金娥[1] 

机构地区：[1]红河学院数学学院,云南蒙自661199

出　　处：《辽宁工程技术大学学报（自然科学版）》2014年第5期691-695,共5页Journal of Liaoning Technical University (Natural Science)

基　　金：国家自然科学基金资助项目(11301160);云南省科技厅自然科学基金资助项目(2013FZ116);云南省教育厅科研基金资助项目(2011C121)

摘　　要：针对经典风险模型中保费收入过程是时间的线性函数这一局限性,建立常数红利边界策略下带扰动的双复合Poisson风险模型,其中保险公司的保费收入是一个复合Poisson过程且与理赔过程相互独立.利用全期望公式及盈余过程的马氏性,得到了直至破产时红利付款的期望现值、矩母函数、n阶矩以及模型的期望折现罚金函数所满足的积分—微分方程及边界条件.In order to overcome the limitations of classical risk that the premium income process is a linear function of time, this paper considered a double compound Poisson risk model perturbed by diffusion where the premium income process is a compound Poisson process and it is also independent of the claim process, moreover,there is a constant dividend barrier strategy in this model. The integro-differential equations with boundary conditions for the expectation, the moment generating function and the nth moment of the discounted dividend payments until ruin are obtained in terms of the total expectation formula and the strong Markov property of thesurplus process. Furthermore, the integro-differential equation with boundary conditions for the Gerber-Shiu function was derived. The study results provide certain guiding significance for the insurance company management decision.

关 键 词：复合POISSON过程 风险模型 BROWN运动 常红利边界 红利付款 矩母函数 期望折现罚金函数 积分-微分方程 

分 类 号：O211.67[理学—概率论与数理统计]