On maximizing expected discounted taxation in a risk process with interest

In risk theory, the problem of maximizing the expected cumulated discounted loss-carry-forward tax payments until ruin is a widely discussed topic since the taxation system was proposed by Albrecher and Hipp (2007). In the present paper, we discuss this maximization problem in the Cramér–Lundberg risk model including a constant force of interest. The optimal taxation return function is identified as the classical solution of the associated Hamilton–Jacobi–Bellman equation and the optimal taxation strategy in this risk model with interest is derived, which is of band type. Finally, an example is constructed for exponential claim sizes, in which closed-form expression for the optimal taxation return function is given.