Lundberg’s risk process with tax

In this paper we extend the classical Cramér–Lundberg risk model by including tax payments. The considered tax rule is to pay a certain proportion of the premium income, whenever the portfolio is in a profitable situation. It is shown that the resulting survival probability is a power of the survival probability without tax. Furthermore, an explicit expression for the expected discounted total sum of tax payments until ruin according to this taxation rule is derived and the optimal starting level for taxation is determined. Finally, numerical illustrations of the results are given for the case of exponential claim amounts.