Optimal Dividend Strategy under the Risk Model with Stochastic Premium

In contrast with the classical Cramer-Lundberg model where the premium process is a linear function of time, we consider the constant barrier strategy under the risk model where the aggregate premium process is modeled as a compound Poisson process. Dickson and Waters (2004) pointed out that the shareholders should be liable to cover the deficit at ruin. Thus, the optimization criteria considered in this paper is maximizing the expectation of the difference between discounted dividends until ruin and the deficit at ruin. As an illustration, the condition of the optimal barrier is calculated in the case where the individual stochastic premium amount and claim amount are exponential distributed.