The compound Pascal model with dividends paid under random interest

Consider a discrete time risk model under random interest based on the compound Pascal model. The insurer pays a dividend of 1 with a probability q0 when the surplus is greater than or equal to a non-negative b. In addition, the effect of interest is considered in our model. We derive recursion formulas for the ruin probability, and the joint distribution of the surplus before ruin and the deficit at ruin. Further, we give the generalized Lundberg inequalities for the ruin probability when q0=1.