两步保费率下的Erlang（2）风险过程

本文研究了两步保费率下Erlang(2)风险过程,给出了Gerber-Shiu折现罚函数的两个微积分方程及其解或更新方程.在索赔额为指数分布条件下得到了两个与破产相关的量并计算出了相应的数值结果.

Erlang (2) Risk Process with Two-step Premium Rate

We consider the Erlang (2) risk model with threshold dividend strategy. Under this strategy, no dividends are paid if the insurer's surplus is below certain threshold barrier. When the surplus is above this barrier, dividends are paid at a rate less than the premium rate. Two integro-defferential equations for the Gerber-Shiu discounted penalty function are given, and also their solutions are utilized to derive the probability of ultimate ruin and the Laplace transformation of the time of ruin where the claim size distribution is exponential. A numerical example is given for illustration.