1 Department of Mathematical Sciences, Faculty of Science, Københavns Universitet2 Department of Mathematics, University of Bergen, Norway3 Department of Mathematical Sciences, Faculty of Science, Københavns Universitet
his paper addresses the problem of finding an optimal dividend policy for a class of jump-diffusion 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. Each dividend payment is changed by a fixed and a proportional cost, meaning that if ξ is paid out by the company, the shareholders receive kξ−K, where k and K are positive. The aim is to maximize expected discounted dividends until ruin. It is proved that when the jumps belong to a certain class of light-tailed distributions, the optimal policy is a simple lump sum policy, that is, when assets are equal to or larger than an upper barrier u¯∗, they are immediately reduced to a lower barrier u−∗ through a dividend payment. The case with K=0 is also investigated briefly, and the optimal policy is shown to be a reflecting barrier policy for the same light-tailed class. Methods to numerically verify whether a simple lump sum barrier strategy is optimal for any jump distribution are provided at the end of the paper, and some numerical examples are given.
Finance and Stochastics, 2013, Vol 17, Issue 1, p. 73-106