When does surplus reach a given target before ruin in the Markov-modulated diffusion model?

In this paper, we consider a Markov-modulated diffusion risk model. We study when the surplus reaches a given level b(U(0)) before ruin. We show that the Laplace transform of such random time can be expressed via the expected discounted penalty functions. Finally, we modify the Markov-modulated diffusion model by a barrier dividend strategy, and give some expressions for the expected discounted penalty functions and the expected discounted dividend payments.