The Distribution of the Maximum Surplus before Ruin for Two Classes of Perturbed Risk Model with Stochastic Income

In this paper, we consider the two classes of perturbed risk model with stochastic income. We set up the integro-differential equations for the distribution of the maximum surplus before ruin $\mathscr{G}(u;d). The Laplace transforms of $\mathscr{G}(u;d),d\rightarrow+\infty are obtained for exponential premium income. The explicit expressions for the distribution of the maximum surplus before ruin are derived when the two classes claim amount distributions all belong to the rational family.