Dividend Payments under the Risk Model with Stochastic Premium and Constant Interest

In this paper, we consider a risk model where the aggregate premium process is a compound Poisson process. Moreover, there are a constant interest and a constant dividend barrier strategy in this model. The integro-differential equations for the expectation and the nth moment and the moment generating function of the cumulative discounted dividend payments until ruin are obtained. Meanwhile, the explicit expressions for the expectation and the nth moment and the moment generating function of the cumulative dividend payments until ruin are given when the individual stochastic premium amount and claim amount are exponentially distributed. Finally, numerical example is also given to illustrate the effect of the related parameters on the expected value of the cumulative discounted dividend payments until ruin.