Optimal dividend policies with transaction costs for a class of jump-diffusion processes

In the talk we will address the problem of finding an optimal dividend policy for a class of jumpdiffusion processes. The jump component is a compound Poisson process with negative jumps, and the drift and diffusion components are assumed to satisfy some regularity and growth restrictions. With each dividend payment there is associated a fixed and a proportional cost. The aim is to maximize expected discounted dividends until ruin. A main result is that when the jumps belong to a certain class of light tailed distributions, the optimal policy is a simple lump sum policy. This means that when assets are equal to or larger than an upper barrier ū*, they are immediately reduced to a lower barrier u* through a dividend payment. Methods to numerically verify whether a simple lump sum barrier strategy is optimal for any jump distribution are provided, and some numerical examples are given. These indicate that a simple lump sum dividend barrier strategy can be optimal for quite a large class of jump distributions.