复合Poisson模型中“双界限”分红问题

Compound Poisson risk model with double-threshold dividend strategy

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 ...