Optimal dividends in the Brownian motion risk model with interest

Authors:
Ying Fang;Rong Wu
Affiliations:
Department of Mathematics and LPMC, Nankai University, Tianjin 300071, PR China;Department of Mathematics and LPMC, Nankai University, Tianjin 300071, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 3
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Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
On optimal dividends: from reflection to refraction

Journal of Computational and Applied Mathematics - Special issue: Jef Teugels

An optimal dividend strategy in the discrete Sparre Andersen model with bounded dividend rates

Journal of Computational and Applied Mathematics

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Abstract

In this paper, we consider a Brownian motion risk model, and in addition, the surplus earns investment income at a constant force of interest. The objective is to find a dividend policy so as to maximize the expected discounted value of dividend payments. It is well known that optimality is achieved by using a barrier strategy for unrestricted dividend rate. However, ultimate ruin of the company is certain if a barrier strategy is applied. In many circumstances this is not desirable. This consideration leads us to impose a restriction on the dividend stream. We assume that dividends are paid to the shareholders according to admissible strategies whose dividend rate is bounded by a constant. Under this additional constraint, we show that the optimal dividend strategy is formed by a threshold strategy.