TY - JOUR
T1 - Optimal dividend policies with transaction costs for a class of jump-diffusion processes
AU - Hunting, Martin
AU - Paulsen, Jostein
PY - 2013/1
Y1 - 2013/1
N2 - This 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 ū*, 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.
AB - This 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 ū*, 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.
U2 - 10.1007/s00780-012-0186-z
DO - 10.1007/s00780-012-0186-z
M3 - Journal article
SN - 0949-2984
VL - 17
SP - 73
EP - 106
JO - Finance and Stochastics
JF - Finance and Stochastics
IS - 1
ER -