Dividend problems in the dual risk model with exponentially distributed observation time

In this paper, we consider the dual of the compound Poisson risk model with exponentially distributed observation time and constant dividend barrier strategy. We derive and solve the integro-differential equations satisfied by the expected total discounted dividend payments until ruin and ruin probability when the gains follow an exponential distribution. Moreover, numerical illustrations for the effect of random observation time on the expected value of the discounted sum of all dividend payments until ruin and ruin probability are studied.