中文摘要：

本文考虑变保费风险模型,假设保费率是随时间变化的,研究了其Gerber-Shiu惩罚函数.通过无穷小方法给出Gerber-Shiu惩罚函数所满足的积分-微分方程;在指数索赔下,给出其破产时赤字的数学期望及破产时的拉普拉斯变换.

英文摘要：

In this article, we consider the risk model in which the premium rate is assumed to depend upon time. Under this condition, we consider the Gerber-Shiu discounted penalty function for this risk model. By using ＂diffential argument＂, an integro-differential equation for Gerber-Shiu discounted penalty function is given, and is also solved in some special cases.