Joint Distribution of Surplus Immediately before Ruin and the Deficit at Ruin under Interest Force

In this paper we consider a compound Poisson risk model with a constant interest force. We investigate the joint distribution of the surplus immediately before and after ruin. By adapting the techniques in Sundt and Teugels (1995), we obtain integral equations satisfied by the joint distribution function and a Lundberg-type inequality. In the case of zero initial reserve and the case of exponential claim sizes, we obtain explicit expressions for the joint distribution function.