常利率下有阈红利边界的复合Poisson风险模型

The compound Poisson risk model with a threshold strategy under constant interest

考虑了常利率下有阈红利边界的复合Poisson风险模型,给出了罚金折现期望函数满足的积分-微分方程及带干扰的情况下罚金折现函数所满足的积分-微分方程.利用全概率公式得到了相应积分-微分方程的解、破产概率及破产前瞬时盈余和破产赤字的联合分布的具体表达式.该模型有利于降低公司最终破产的概率.

In this paper,it is considered that the expected discounted penalty function for compound Poisson risk process with a threshold strategy under constant interest.Firstly the integro-differential equations and the explicit solution to the integro-differential equations are derived.Secondly the expressions for the ruin probability and the joint distribution of the surplus immediately before ruin and the deficit at ruin are given.Finally it is obtained that the integro-differential equations satisfied by the expected discounted penalty function when the risk process perturbed by diffusion.