Dividend Payments in Jump-Diffusion Risk Model with Interest and Constant Dividend Barrier

This article considers the compound Poisson insurance risk model perturbed by diffusion with investment and constant dividend barrier. Integro-differential equations for the high order moments of the discounted dividend payments prior to ruin are derived. Closed form solutions are formulated when the individual claim amount distribution is exponential. Some satisfying results about the distribution of the aggregate dividend are obtained, even for general claim size distributions. We also investigate the number and the amount of the dividend streams. Both the time of ruin and the deficit at ruin are considered in some special cases. Confluent hypergeometric functions play a key role in this paper.