IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v47y2016i3d10.1007_s10614-015-9502-y.html
   My bibliography  Save this article

A Non-stationary Model of Dividend Distribution in a Stochastic Interest-Rate Setting

Author

Listed:
  • Andrea Barth

    (ETH Zürich
    University of Stuttgart)

  • Santiago Moreno–Bromberg

    (University Zürich)

  • Oleg Reichmann

    (ETH Zürich)

Abstract

In this paper the solutions to several variants of the so-called dividend-distribution problem in a multi-dimensional, diffusion setting are studied. In a nutshell, the manager of a firm must balance the retention of earnings (so as to ward off bankruptcy and earn interest) and the distribution of dividends (so as to please the shareholders). A dynamic-programming approach is used, where the state variables are the current levels of cash reserves and of the stochastic short-rate, as well as time. This results in a family of Hamilton–Jacobi–Bellman variational inequalities whose solutions must be approximated numerically. To do so, a finite element approximation and a time-marching scheme are employed.

Suggested Citation

  • Andrea Barth & Santiago Moreno–Bromberg & Oleg Reichmann, 2016. "A Non-stationary Model of Dividend Distribution in a Stochastic Interest-Rate Setting," Computational Economics, Springer;Society for Computational Economics, vol. 47(3), pages 447-472, March.
  • Handle: RePEc:kap:compec:v:47:y:2016:i:3:d:10.1007_s10614-015-9502-y
    DOI: 10.1007/s10614-015-9502-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10614-015-9502-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10614-015-9502-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Julien Hugonnier & Semyon Malamud & Erwan Morellec, 2015. "Capital Supply Uncertainty, Cash Holdings, and Investment," The Review of Financial Studies, Society for Financial Studies, vol. 28(2), pages 391-445.
    3. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," The Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    4. Patrick Bolton & Hui Chen & Neng Wang, 2014. "Debt, Taxes, and Liquidity," NBER Working Papers 20009, National Bureau of Economic Research, Inc.
    5. Pablo Azcue & Nora Muler, 2005. "Optimal Reinsurance And Dividend Distribution Policies In The Cramér‐Lundberg Model," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 261-308, April.
    6. Radner, Roy & Shepp, Larry, 1996. "Risk vs. profit potential: A model for corporate strategy," Journal of Economic Dynamics and Control, Elsevier, vol. 20(8), pages 1373-1393, August.
    7. Jean-Charles Rochet & Stéphane Villeneuve, 2005. "Corporate portfolio management," Annals of Finance, Springer, vol. 1(3), pages 225-243, August.
    8. Dumas, Bernard, 1991. "Super contact and related optimality conditions," Journal of Economic Dynamics and Control, Elsevier, vol. 15(4), pages 675-685, October.
    9. Hipp, Christian & Plum, Michael, 2000. "Optimal investment for insurers," Insurance: Mathematics and Economics, Elsevier, vol. 27(2), pages 215-228, October.
    10. Brennan, Michael J & Schwartz, Eduardo S, 1977. "The Valuation of American Put Options," Journal of Finance, American Finance Association, vol. 32(2), pages 449-462, May.
    11. Pablo Azcue & Nora Muler, 2010. "Optimal investment policy and dividend payment strategy in an insurance company," Papers 1010.4988, arXiv.org.
    12. Løkka, Arne & Zervos, Mihail, 2008. "Optimal dividend and issuance of equity policies in the presence of proportional costs," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 954-961, June.
    13. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    14. Zhengjun Jiang & Martijn Pistorius, 2012. "Optimal dividend distribution under Markov regime switching," Finance and Stochastics, Springer, vol. 16(3), pages 449-476, July.
    15. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(4), pages 419-438, December.
    16. Bjarne Højgaard & Michael Taksar, 2004. "Optimal dynamic portfolio selection for a corporation with controllable risk and dividend distribution policy," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 315-327.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Klimenko, Nataliya & Moreno-Bromberg, Santiago, 2016. "The shadow costs of repos and bank liability structure," Journal of Economic Dynamics and Control, Elsevier, vol. 65(C), pages 1-29.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    2. Décamps, Jean-Paul & Villeneuve, Stéphane, 2022. "Learning about profitability and dynamic cash management," Journal of Economic Theory, Elsevier, vol. 205(C).
    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. Alex S. L. Tse, 2020. "Dividend policy and capital structure of a defaultable firm," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 961-994, July.
    5. Elena Bandini & Tiziano De Angelis & Giorgio Ferrari & Fausto Gozzi, 2022. "Optimal dividend payout under stochastic discounting," Mathematical Finance, Wiley Blackwell, vol. 32(2), pages 627-677, April.
    6. Gerrard, Russell & Kyriakou, Ioannis & Nielsen, Jens Perch & Vodička, Peter, 2023. "On optimal constrained investment strategies for long-term savers in stochastic environments and probability hedging," European Journal of Operational Research, Elsevier, vol. 307(2), pages 948-962.
    7. Julia Eisenberg & Stefan Kremsner & Alexander Steinicke, 2021. "Two Approaches for a Dividend Maximization Problem under an Ornstein-Uhlenbeck Interest Rate," Papers 2108.00234, arXiv.org.
    8. Christensen, Bent Jesper & Parra-Alvarez, Juan Carlos & Serrano, Rafael, 2021. "Optimal control of investment, premium and deductible for a non-life insurance company," Insurance: Mathematics and Economics, Elsevier, vol. 101(PB), pages 384-405.
    9. Décamps, Jean-Paul & Mariotti, Thomas & Rochet, Jean-Charles & Villeneuve, Stéphane, 2008. "Free Cash-Flow, Issuance Costs and Stock Price Volatility," IDEI Working Papers 518, Institut d'Économie Industrielle (IDEI), Toulouse.
    10. Tiziano De Angelis, 2018. "Optimal dividends with partial information and stopping of a degenerate reflecting diffusion," Papers 1805.12035, arXiv.org, revised Mar 2019.
    11. Hugonnier, Julien & Morellec, Erwan, 2017. "Bank capital, liquid reserves, and insolvency risk," Journal of Financial Economics, Elsevier, vol. 125(2), pages 266-285.
    12. Gunther Leobacher & Michaela Szolgyenyi & Stefan Thonhauser, 2016. "Bayesian Dividend Optimization and Finite Time Ruin Probabilities," Papers 1602.04660, arXiv.org.
    13. Jonathan Ziveyi, 2011. "The Evaluation of Early Exercise Exotic Options," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 12, July-Dece.
    14. Julia Eisenberg & Yuliya Mishura, 2018. "An Exponential Cox-Ingersoll-Ross Process as Discounting Factor," Papers 1808.10355, arXiv.org.
    15. Julia Eisenberg & Zbigniew Palmowski, 2020. "Optimal Dividends Paid in a Foreign Currency for a L\'evy Insurance Risk Model," Papers 2001.03733, arXiv.org.
    16. Chuang-Chang Chang & Jun-Biao Lin & Wei-Che Tsai & Yaw-Huei Wang, 2012. "Using Richardson extrapolation techniques to price American options with alternative stochastic processes," Review of Quantitative Finance and Accounting, Springer, vol. 39(3), pages 383-406, October.
    17. Giorgio Ferrari & Patrick Schuhmann, 2018. "An Optimal Dividend Problem with Capital Injections over a Finite Horizon," Papers 1804.04870, arXiv.org, revised May 2019.
    18. Broadie, Mark & Detemple, Jerome & Ghysels, Eric & Torres, Olivier, 2000. "American options with stochastic dividends and volatility: A nonparametric investigation," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 53-92.
    19. Julia Eisenberg & Stefan Kremsner & Alexander Steinicke, 2021. "Two Approaches for a Dividend Maximization Problem under an Ornstein-Uhlenbeck Interest Rate," Mathematics, MDPI, vol. 9(18), pages 1-20, September.
    20. Koch-Medina, Pablo & Moreno-Bromberg, Santiago & Ravanelli, Claudia & Šikić, Mario, 2021. "Revisiting optimal investment strategies of value-maximizing insurance firms," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 131-151.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:compec:v:47:y:2016:i:3:d:10.1007_s10614-015-9502-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.