中文摘要：

本文研究了包含两类相关风险和模型的Gerber-Shiu函数，利用积分-微分方程和构造指数鞅，获得了破产时Gerber-Shiu函数的Laplace变换，当两类索赔额均服从指数分布时，求出了相应的显式。

英文摘要：

The Gerber-Shiu functions for a risk model involving two dependent classes of risk processes is discussed in this paper. We get Laplace transforms of two types of the Gerber-Shiu functions at ruin by an integro-differential equation in terms of constructing martingale. Explicit results are derived when the claims from both classes are exponentially distributed.