Lvy运动干扰的经典风险模型的Gerber-Shiu函数

The Gerber-Shiu Function for a Risk Model Perturbed by Stable Lvy Motion

通过一个弱收敛方法,本文首次以拉普拉斯变换的形式给出α-稳定Levy运动干扰的经典风险模型的Gerber-Shiu期望折扣惩罚函数(G-S函数).用同样的方法,也获得了这个风险模型的最终破产概率作为本文结果的补充.作为检验,这个风险过程的最终破产概率实际上是G-S函数的特殊情形.

By following a weak convergence approach, the present paper for the first time gives the representation of the Gerber-Shiu expected discounted penalty function （the G-S function） of the risk process perturbed by an α-stable Levy motion in terms of the Laplace transform. Using the same method, this paper also gives the ultimate ruin probability as a byproduct of our results. As a check, we find that the ultimate ruin probability of the risk process is indeed a special case of the G-S function.