DSA Seminars - Hanspeter Schmidli (University of Cologne, Germany)

We consider a risk model driven by a spectrally negative Lévy process. From the surplus dividends are paid and capital injections have to be made in order to keep the surplus positive. In addition, tax has to be paid for dividends, but injections lead to an exemption from tax. We generalise the results for the diffusion approximation and for the classical model, and show that the optimal dividend strategy is a two barrier strategy. The barrier depends on whether an immediate dividend would be taxed or not. For a risk process perturbed by diffusion with exponentially distributed claim sizes we show how the value function and the barriers can be determined.