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

Martin Hunting () and Jostein Paulsen ()

Finance and Stochastics, 2013, vol. 17, issue 1, 73-106

Abstract: 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 $\bar{u}^{*}$ , they are immediately reduced to a lower barrier $\underline{u}^{*}$ 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. Copyright Springer-Verlag 2013

Keywords: Optimal dividends; Jump-diffusion models; Impulse control; Barrier strategy; Singular control; Numerical solution; 49N25; 45J05; 60J99; 91G80; 93E20; C61 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s00780-012-0186-z

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