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Discrete Dividend Payments in Continuous Time

Author

Listed:
  • Jussi Keppo

    (Business School and Institute of Operations Research and Analytics, National University of Singapore, Singapore 119245)

  • A. Max Reppen

    (Questrom School of Business, Boston University, Boston, Massachusetts 02215)

  • H. Mete Soner

    (Operations Research and Financial Engineering Department, Princeton University, Princeton, New Jersey 08544)

Abstract

We propose a model in which dividend payments occur at regular, deterministic intervals in an otherwise continuous model. This contrasts traditional models where either the payment of continuous dividends is controlled or the dynamics are given by discrete time processes. Moreover, between two dividend payments, the structure allows for other types of control; we consider the possibility of equity issuance at any point in time. The value is characterized as the fixed point of an optimal control problem with periodic initial and terminal conditions. We prove the regularity and uniqueness of the corresponding dynamic programming equation and the convergence of an efficient numerical algorithm that we use to study the problem. The model enables us to find the loss caused by infrequent dividend payments. We show that under realistic parameter values, this loss varies from around 1%–24% depending on the state of the system and that using the optimal policy from the continuous problem further increases the loss.

Suggested Citation

  • Jussi Keppo & A. Max Reppen & H. Mete Soner, 2021. "Discrete Dividend Payments in Continuous Time," Mathematics of Operations Research, INFORMS, vol. 46(3), pages 895-911, August.
    • Handle: RePEc:inm:ormoor:v:46:y:2021:i:3:p:895-911
    DOI: 10.1287/moor.2020.1081
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    References listed on IDEAS

    as
    1. Avanzi, Benjamin & Tu, Vincent & Wong, Bernard, 2016. "On The Interface Between Optimal Periodic And Continuous Dividend Strategies In The Presence Of Transaction Costs," ASTIN Bulletin, Cambridge University Press, vol. 46(3), pages 709-746, September.
    2. Akyildirim, Erdinç & Güney, I. Ethem & Rochet, Jean-Charles & Soner, H. Mete, 2014. "Optimal dividend policy with random interest rates," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 93-101.
    3. A. Max Reppen & Jean‐Charles Rochet & H. Mete Soner, 2020. "Optimal dividend policies with random profitability," Mathematical Finance, Wiley Blackwell, vol. 30(1), pages 228-259, January.
    4. Samu Peura & Jussi Keppo, 2006. "Optimal Bank Capital with Costly Recapitalization," The Journal of Business, University of Chicago Press, vol. 79(4), pages 2163-2202, July.
    5. Jean‐Paul Décamps & Thomas Mariotti & Jean‐Charles Rochet & Stéphane Villeneuve, 2011. "Free Cash Flow, Issuance Costs, and Stock Prices," Journal of Finance, American Finance Association, vol. 66(5), pages 1501-1544, October.
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    Cited by:

    1. Chonghu Guan & Zuo Quan Xu, 2026. "Dividend ratcheting and capital injection under the Cram\'er-Lundberg model: Strong solution and optimal strategy," Papers 2604.04641, arXiv.org.
    2. Min Dai & Steven Kou & H. Mete Soner & Chen Yang, 2023. "Leveraged Exchange-Traded Funds with Market Closure and Frictions," Management Science, INFORMS, vol. 69(4), pages 2517-2535, April.

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