跳扩散对偶模型在带壁分红策略下的分红函数  

Dividend Function in the Jump-Diffusion Dual Model With Barrier Dividend Strategy

作　　者：李波[1] 吴荣[1] 

机构地区：[1]南开大学数学科学学院,天津300071

出　　处：《应用数学和力学》2008年第9期1124-1134,共11页Applied Mathematics and Mechanics

基　　金：国家重点基础研究发展计划(973计划)资助项目(2007CB814905);国家自然科学基金资助项目(10571092);高等教育博士学科点科研基金资助项目

摘　　要：考虑了带干扰的古典风险模型的对偶模型,讨论了模型在带壁分红策略下的一些结论.通过研究过程的局部时,证明了所讨论函数的边界条件.用在没有分红策略下模型的函数,给出了期望折现分红函数的显示表达.在最后一节,对于跳服从相位分布的情形,给出了数值例子,并讨论了最优分红边界的存在性.A dual model of the perturbed classical corapound Poisson risk model under a constant div- idend barrier was considered. A new method is used in deriving the boundary condition of the equation satisfied by that expectation function, by using the local time of a related process. The expression for the expected discounted dividend function was obtained in terms of those in the corresponding perturbed corapound Poisson risk model without barrier. The special cases where the gain size is phasetype distributed is illustrated in the last section. Also the existence of the optimal dividend level was considered.

关 键 词：复合POISSON过程 扩散过程 GERBER-SHIU函数 微分积分方程 破产时 破产前余额 赤字 

分 类 号：O211.6[理学—概率论与数理统计]