Distributional study of finite-time ruin related problems for the classical risk model

In this paper, we study some finite-time ruin related problems for the classical risk model. We demonstrate that some techniques recently developed in [37] and [6] can be used to study the joint distribution of the time of ruin and the maximum surplus prior to ruin, the joint distribution of the time of ruin and the maximum severity of ruin, and the distribution of the two-sided first exit time. Especially, by solving a Seal's type partial integro-differential equation we obtain an explicit (integral) expression for the finite-time Gerber-Shiu function, which is expressed in terms of the (infinite time) Gerber-Shiu function introduced in [12].