The optimal dividend barrier in the perturbed compound Poisson risk model with randomized observation time

This paper considers the dividend problems in the perturbed compound Poisson risk model. Assume that dividends can only be paid at the observation time when the surplus exceeds the barrier level and the excess is paid as dividend. In this paper, integro-differential equations for the expected discounted dividends until ruin and the Laplace transform of ruin time are firstly derived. When the claim is exponentially distributed, explicit expressions for the expected discounted dividends until ruin and the Laplace transform of ruin time are also obtained. Finally, the optimal dividend barrier which maximizes the expected discounted dividends until ruin is given.