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Optimal dividend strategies in a dual model with capital injections

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Abstract

We study three types of practical optimization problems faced by a firm that can control its liquid reserves by paying dividends and by issuing new equity. In the first problem, we consider the classical dividend problem without equity issuance. The second problem aims at maximizing the expected discounted dividend payments minus the expected discounted costs of issuing new equity over strategies associated with positive reserves at all times. The third problem has the same objective as the second one, but with no constraints on the reserves. Under the assumption of proportional transaction costs, we identify the value functions and the optimal strategies. We also present the relationship between three problems.

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Authors and Affiliations

  1. Department of Mathematics, Central South University, No. 22 South Shaoshan Road, 410075, Changsha, Hunan, China

    Hongshuai Dai & Zaiming Liu

  2. School of Mathematical Sciences, Beijing Normal University, 100875, Beijing, China

    Nana Luan

Authors
  1. Hongshuai Dai
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  2. Zaiming Liu
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  3. Nana Luan
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Correspondence to Hongshuai Dai.

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Dai, H., Liu, Z. & Luan, N. Optimal dividend strategies in a dual model with capital injections. Math Meth Oper Res 72, 129–143 (2010). https://doi.org/10.1007/s00186-010-0312-7

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  • DOI: https://doi.org/10.1007/s00186-010-0312-7

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