带干扰的两类理赔更新风险模型的Gerber-Shiu函数

Gerber-Shiu Functions for a Perturbed Renewal Risk Model with Two Classes of Claims

考虑一类带干扰的两类理赔更新风险模型,假设两类理赔的到来过程都是以时间间隔为Phase分布的更新过程,得到了Gerber-Shiu函数满足的积分微分方程及其解析解,并且当两类理赔额的密度函数均属于有理分布族时,给出了一些具体表达式.

We considered a perturbed renewal risk model with two classes of claims, for which both the two claim number processes are renewal processes with Phase inter-claim time. We derived the integro-differential equations of the Gerber-Shiu functions and obtained the analytical solutions, and when the densities of the two classes of Claims belong to rational family, we got some explicit expressions. Finally, we gave a numerical example to illustrate theses results.