Some Distributions for Risk Process Perturbed by Diffusion under Interest Force

We consider the risk process perturbed by diffusion under interest force in this article. The integral expressions, continuities, twice continuous differentiability and integro-differential equations about F_\delta(u;x), the distribution of the surplus immediately before ruin, and H_\delta(u;x,y), the joint distribution of the surplus immediately before ruin and the deficit at ruin are obtained. As corollaries, some distributions for the classical risk process that is perturbed by diffusion are also considered. Certainly, it is seen that many results in references may be derived from our conclusions by letting some constant variable zero.