中文摘要：

考虑带扰动的两类相关索赔风险过程．把相关的两类索赔计数过程通过模型转换为独立的Poisson—Geometric和广义Erlang（n）计数过程．得到了此模型的折现罚金函数的积分微分方程和该模型的折现罚金函数的Laplace变换，并且当相关两类索赔的密度函数的Laplace变换为有理函数时，给出了折现罚金函数的具体表达式．

英文摘要：

A risk model with dependent classes of insurance business was considered. The correlated two claims in the counting process were transformed through model into independent Possion-Geometric and generalized Erlang（n） processes. Firstly, integro-differential equations satisfied by the expected discounted penalty function were derived by changing the model into two independent models. Secondly, the Laplace transforms and the explicit expressions of the Gerber-shiu discounted penalty function were derived. Finally, some explicit expressions for the Gerber-shiu discounted penalty functions with positive initial surplus were given with the densities of two classes of claim distributions being rational Laplace transforms.