The dividend function in the jump-diffusion dual model with barrier dividend strategy

A dual model of the perturbed classical compound Poisson risk model is considered under a constant dividend barrier.A new method is used in deriving the boundary condition of the equation for the expectation function by studying the local time of a related process.We obtain the expression for the expected discount dividend function in terms of those in the corresponding perturbed compound Poisson risk model without barriers.A special case in which the gain size is phase-type distributed is illustrated.We also consider the existence of the optimal dividend level.