复合Poisson模型中“双界限”分红问题  

Compound Poisson risk model with double-threshold dividend strategy

作　　者：高合理[1,2] 尹传存[2] 

机构地区：[1]滨州学院数学与信息科学系,山东滨州256603 [2]曲阜师范大学数学科学学院,山东曲阜273165

出　　处：《高校应用数学学报（A辑）》2008年第4期379-388,共10页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(10771119);教育部科技重点项目(206091)

摘　　要：引入了复合Poisson模型中的"双界限"分红模型,在这种模型中,当盈余超过上限时分红以不超过保费率的速率付出,低于下限后保费率增大.文中利用Gerber- Shiu函数来分析这种模型,先导出了Gerber-Shiu函数m_1,m_2,m_3满足的积分-微分方程,再给出m_1,m_2,m_3的解析表示,最后通过几步把Gerber-Shiu函数m(u;b_1,b)的解析式表示出来.In this paper,the classical compound Poisson risk model with a double-threshold dividend strategy is considered.Under such a strategy,when the surplus is above the upper barrier, dividends are paid at a constant rate that does not exceed the premium rate,and the premium rate increases if the surplus falls below the lower barrier.Three integro-differential equations for the Gerber- Shiu discounted penalty function are derived,and analytical expressions for the Gerber-Shiu discounted penalty function m_1,m_2 ...

关 键 词：复合Poisson模型 THRESHOLD strategy模型 GERBER-SHIU函数 积分-微分方程 更新方程 

分 类 号：O175[理学—数学]