On a risk model with Markovian arrivals and tax

A risk model with Markovian arrivals and tax payments is considered. When the insurer is in a profitable situation, the insurer may pay a certain proportion of the premium income as tax payments. First, the Laplace transform of the time to cross a certain level before ruin is discussed. Second, explicit formulas for a generalized Gerber-Shiu function are established in terms of the ??original?? Gerber-Shiu function without tax and the Laplace transform of the first passage time before ruin. Finally, the differential equations satisfied by the expected accumulated discounted tax payments until ruin are derived. An explicit expression for the discounted tax payments is also given.