An optimal dividends problem with transaction costs for spectrally negative Levy processes

We consider an optimal dividends problem with transaction costs where the reserves are modeled by a spectrally negative Levy process. We make the connection with the classical de Finetti problem and show in particular that when the Levy measure has a log-convex density, then an optimal strategy is given by paying out a dividend in such a way that the reserves are reduced to a certain level c(1) whenever they are above another level c(2). Further we describe a method to numerically find the optimal values of c(1) and c(2). (C) 2009 Elsevier B.V. All rights reserved.