ON A CLASS OF STATIONARY RENEWAL RISK MODEL WITH CONSTANT DIVIDEND BARRIER

In this paper, we discuss the expected discounted penalty function with a constant dividend barrier at ruin under the stationary renewal risk process. By strong Markov property, we first show that the expected discounted penalty function satisfies an integro-differential equation. We further prove that the solution to this equation can be expressed by the penalty function with a constant dividend barrier at ruin under ordinary renewal risk model. An explicit expression for the solution of this equation can be derived.