Optimal Dividend Policies with Transaction Costs for a Class of Diffusion Processes

Lihua Bai; Jostein Paulsen

doi:10.1137/090773210

Optimal Dividend Policies with Transaction Costs for a Class of Diffusion Processes

Lihua Bai, Jostein Paulsen

Department of Mathematical Sciences

12 Citations (Scopus)

Abstract

Finding optimal dividend strategies is a classical problem in the financial and actuarial literature. The idea is that the company wants to pay some of its surplus as dividends, and the problem is to find a dividend strategy that maximizes the expected total discounted dividends received by the shareholders until ruin. Here we generalize results in [J. Paulsen, Adv. Appl. Probab., 39 (2007), pp. 669-689] in that the rate of growth of the surplus process is assumed to exceed the discounting factor whenever the surplus process is smaller than a fixed number λ. In [J. Paulsen, Adv. Appl. Probab., 39 (2007), pp. 669-689] it was assumed th at this rate of growth is always less than or equal to the discounting factor. It turns out that thi s generalization makes the problem much more complicated, and a simple barrier strategy is no longer always optimal.

Original language	English
Journal	SIAM Journal of Control and Optimization
Volume	48
Issue number	8
Pages (from-to)	4987-5008
Number of pages	22
DOIs	https://doi.org/10.1137/090773210
Publication status	Published - 2010

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abstract = "Finding optimal dividend strategies is a classical problem in the financial and actuarial literature. The idea is that the company wants to pay some of its surplus as dividends, and the problem is to find a dividend strategy that maximizes the expected total discounted dividends received by the shareholders until ruin. Here we generalize results in [J. Paulsen, Adv. Appl. Probab., 39 (2007), pp. 669-689] in that the rate of growth of the surplus process is assumed to exceed the discounting factor whenever the surplus process is smaller than a fixed number λ. In [J. Paulsen, Adv. Appl. Probab., 39 (2007), pp. 669-689] it was assumed th at this rate of growth is always less than or equal to the discounting factor. It turns out that thi s generalization makes the problem much more complicated, and a simple barrier strategy is no longer always optimal.",

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AB - Finding optimal dividend strategies is a classical problem in the financial and actuarial literature. The idea is that the company wants to pay some of its surplus as dividends, and the problem is to find a dividend strategy that maximizes the expected total discounted dividends received by the shareholders until ruin. Here we generalize results in [J. Paulsen, Adv. Appl. Probab., 39 (2007), pp. 669-689] in that the rate of growth of the surplus process is assumed to exceed the discounting factor whenever the surplus process is smaller than a fixed number λ. In [J. Paulsen, Adv. Appl. Probab., 39 (2007), pp. 669-689] it was assumed th at this rate of growth is always less than or equal to the discounting factor. It turns out that thi s generalization makes the problem much more complicated, and a simple barrier strategy is no longer always optimal.

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Optimal Dividend Policies with Transaction Costs for a Class of Diffusion Processes

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