IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-02929766.html
   My bibliography  Save this paper

Optimal dividend policies with random profitability

Author

Listed:
  • Max Reppen

    (ETH Zürich - Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich])

  • Jean-Charles Rochet

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Mete Soner

    (ETH Zürich - Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich])

Abstract

We study an optimal dividend problem under a bankruptcy constraint. Firms face a trade-off between potential bankruptcy and extraction of profits. In contrast to previous works, general cash flow drifts, including Ornsteinâ€"Uhlenbeck and CIR processes, are considered. We provide rigorous proofs of continuity of the value function, whence dynamic programming, as well as comparison between discontinuous sub- and supersolutions of the Hamiltonâ€"Jacobiâ€"Bellman equation, and we provide an efficient and convergent numerical scheme for finding the solution. The value function is given by a nonlinear partial differential equation (PDE) with a gradient constraint from below in one direction. We find that the optimal strategy is both a barrier and a band strategy and that it includes voluntary liquidation in parts of the state space. Finally, we present and numerically study extensions of the model, including equity issuance and gambling for resurrection.

Suggested Citation

  • Max Reppen & Jean-Charles Rochet & Mete Soner, 2020. "Optimal dividend policies with random profitability," Post-Print hal-02929766, HAL.
  • Handle: RePEc:hal:journl:hal-02929766
    DOI: 10.1111/mafi.12223
    Note: View the original document on HAL open archive server: https://hal.science/hal-02929766
    as

    Download full text from publisher

    File URL: https://hal.science/hal-02929766/document
    Download Restriction: no

    File URL: https://libkey.io/10.1111/mafi.12223?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
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Abel Cadenillas & Sudipto Sarkar & Fernando Zapatero, 2007. "Optimal Dividend Policy With Mean‐Reverting Cash Reservoir," Mathematical Finance, Wiley Blackwell, vol. 17(1), pages 81-109, January.
    2. Parsiad Azimzadeh & Peter A. Forsyth, 2015. "Weakly chained matrices, policy iteration, and impulse control," Papers 1510.03928, arXiv.org, revised Sep 2017.
    3. 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.
    4. Fama, Eugene F & French, Kenneth R, 2000. "Forecasting Profitability and Earnings," The Journal of Business, University of Chicago Press, vol. 73(2), pages 161-175, April.
    5. Hackbarth, Dirk & Miao, Jianjun & Morellec, Erwan, 2006. "Capital structure, credit risk, and macroeconomic conditions," Journal of Financial Economics, Elsevier, vol. 82(3), pages 519-550, December.
    6. 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.
    7. Jean-Paul Decamps & Thomas Mariotti & Jean-Charles Rocher & Stephane Villeneuve, 2011. "Free Cash Flows, Inssuance Costs and Volatility," Post-Print halshs-00738437, HAL.
    8. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    9. Bolton, Patrick & Chen, Hui & Wang, Neng, 2013. "Market timing, investment, and risk management," Journal of Financial Economics, Elsevier, vol. 109(1), pages 40-62.
    10. 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.
    11. Mark Gertler & R. Glenn Hubbard, 1993. "Corporate Financial Policy, Taxation, and Macroeconomic Risk," RAND Journal of Economics, The RAND Corporation, vol. 24(2), pages 286-303, Summer.
    12. Jun Cai & Hans Gerber & Hailiang Yang, 2006. "Optimal Dividends In An Ornstein-Uhlenbeck Type Model With Credit And Debit Interest," North American Actuarial Journal, Taylor & Francis Journals, vol. 10(2), pages 94-108.
    13. Julien Hugonnier & Semyon Malamud & Erwan Morellec, 2015. "Capital Supply Uncertainty, Cash Holdings, and Investment," Review of Financial Studies, Society for Financial Studies, vol. 28(2), pages 391-445.
    14. Johannes Muhle-Karbe & Max Reppen & H. Mete Soner, 2016. "A Primer on Portfolio Choice with Small Transaction Costs," Papers 1612.01302, arXiv.org, revised May 2017.
    15. 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.
    16. Pauli Murto & Marko Terviö, 2014. "Exit Options And Dividend Policy Under Liquidity Constraints," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55, pages 197-221, February.
    17. Myers, Stewart C., 1977. "Determinants of corporate borrowing," Journal of Financial Economics, Elsevier, vol. 5(2), pages 147-175, November.
    18. Ronald W. Anderson & Andrew Carverhill, 2012. "Corporate Liquidity and Capital Structure," Review of Financial Studies, Society for Financial Studies, vol. 25(3), pages 797-837.
    19. Zhengjun Jiang & Martijn Pistorius, 2012. "Optimal dividend distribution under Markov regime switching," Finance and Stochastics, Springer, vol. 16(3), pages 449-476, July.
    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. Amlys Syahputra Silalahi & Khaira Amalia Fachrudin & Aryanti Sariartha Sianipar & Kharisya Ayu Effendi, 2021. "Analysis of the Bank Specific Factors, Macroeconomics and Oil Price on Dividend Policy," International Journal of Energy Economics and Policy, Econjournals, vol. 11(2), pages 165-171.
    2. Ferrari, Giorgio & Schuhmann, Patrick & Zhu, Shihao, 2022. "Optimal dividends under Markov-modulated bankruptcy level," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 146-172.
    3. 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.
    4. Décamps, Jean-Paul & Villeneuve, Stéphane, 2022. "Learning about profitability and dynamic cash management," Journal of Economic Theory, Elsevier, vol. 205(C).
    5. Chonghu Guan & Jiacheng Fan & Zuo Quan Xu, 2023. "Optimal dividend payout with path-dependent drawdown constraint," Papers 2312.01668, arXiv.org.
    6. Calvia, Alessandro & Ferrari, Giorgio, 2021. "Nonlinear Filtering of Partially Observed Systems Arising in Singular Stochastic Optimal Control," Center for Mathematical Economics Working Papers 651, Center for Mathematical Economics, Bielefeld University.
    7. Giorgio Ferrari & Patrick Schuhmann & Shihao Zhu, 2021. "Optimal Dividends under Markov-Modulated Bankruptcy Level," Papers 2111.03724, arXiv.org, revised Jun 2022.
    8. Ferrari, Giorgio & Schuhmann, Patrick & Zhu, Shihao, 2021. "Optimal Dividends under Markov-Modulated Bankruptcy Level," Center for Mathematical Economics Working Papers 657, Center for Mathematical Economics, Bielefeld University.
    9. Guillermo Peña, 2021. "The key role of quoted spreads in financial services and transactions," Economics and Business Letters, Oviedo University Press, vol. 10(3), pages 208-216.
    10. 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.
    11. Stefan Kremsner & Alexander Steinicke & Michaela Szölgyenyi, 2020. "A Deep Neural Network Algorithm for Semilinear Elliptic PDEs with Applications in Insurance Mathematics," Risks, MDPI, vol. 8(4), pages 1-18, December.

    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. Décamps, Jean-Paul & Villeneuve, Stéphane, 2022. "Learning about profitability and dynamic cash management," Journal of Economic Theory, Elsevier, vol. 205(C).
    2. Bolton, Patrick & Wang, Neng & Yang, Jinqiang, 2019. "Investment under uncertainty with financial constraints," Journal of Economic Theory, Elsevier, vol. 184(C).
    3. 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.
    4. Patrick Bolton & Ye Li & Neng Wang & Jinqiang Yang, 2020. "Dynamic Banking and the Value of Deposits," NBER Working Papers 28298, National Bureau of Economic Research, Inc.
    5. Décamps, Jean-Paul & Gryglewicz, S. & Morellec, E. & Villeneuve, Stéphane, 2015. "Corporate Policies with Temporary and Permanent Shocks," TSE Working Papers 15-552, Toulouse School of Economics (TSE), revised 15 Jun 2016.
    6. Chen, Hui & Xu, Yu & Yang, Jun, 2021. "Systematic risk, debt maturity, and the term structure of credit spreads," Journal of Financial Economics, Elsevier, vol. 139(3), pages 770-799.
    7. Della Seta, Marco & Morellec, Erwan & Zucchi, Francesca, 2020. "Short-term debt and incentives for risk-taking," Journal of Financial Economics, Elsevier, vol. 137(1), pages 179-203.
    8. Strebulaev, Ilya A. & Whited, Toni M., 2012. "Dynamic Models and Structural Estimation in Corporate Finance," Foundations and Trends(R) in Finance, now publishers, vol. 6(1–2), pages 1-163, November.
    9. 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.
    10. Décamps, Jean Paul & Morellec, Erwan & Villeneuve, Stéphane & Gryglewicz, Sebastian, 2015. "Corporate policies with permanent and temporary shocks," CEPR Discussion Papers 10420, C.E.P.R. Discussion Papers.
    11. Lambrecht, Bart M., 2017. "Real options in finance," Journal of Banking & Finance, Elsevier, vol. 81(C), pages 166-171.
    12. Marc Arnold & Dirk Hackbarth & Tatjana Xenia Puhan, 2018. "Financing Asset Sales and Business Cycles [Does industry-wide distress affect defaulted firms? Evidence from creditor recoveries]," Review of Finance, European Finance Association, vol. 22(1), pages 243-277.
    13. Ekaterina Kuzmicheva & Kirill Kuzmichev, 2013. "The influence of financial constraints and real options on corporate investment decisions," HSE Working papers WP BRP 17/FE/2013, National Research University Higher School of Economics.
    14. Hackbarth, Dirk & Rivera, Alejandro & Wong, Tak-Yuen, 2018. "Optimal Short-Termism," CEPR Discussion Papers 12588, C.E.P.R. Discussion Papers.
    15. Etienne Chevalier & Vathana Ly Vath & Alexandre Roch, 2020. "Optimal Dividend and Capital Structure with Debt Covenants," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 535-565, November.
    16. Iván Alfaro & Nicholas Bloom & Xiaoji Lin, 2024. "The Finance Uncertainty Multiplier," Journal of Political Economy, University of Chicago Press, vol. 132(2), pages 577-615.
    17. Hui Chen & Gustavo Manso, 2017. "Macroeconomic Risk and Debt Overhang," Review of Corporate Finance Studies, Oxford University Press, vol. 6(1), pages 1-38.
    18. repec:zbw:bofrdp:2019_018 is not listed on IDEAS
    19. Nikolov, Boris & Schmid, Lukas & Steri, Roberto, 2019. "Dynamic corporate liquidity," Journal of Financial Economics, Elsevier, vol. 132(1), pages 76-102.
    20. Li, Delong & Lu, Lei & Mu, Congming & Yang, Jinqiang, 2019. "Biased beliefs, costly external finance, and firm behavior : A Unified theory," Research Discussion Papers 18/2019, Bank of Finland.
    21. Subrahmanyam, Marti G. & Tang, Dragon Yongjun & Wang, Sarah Qian, 2017. "Credit default swaps, exacting creditors and corporate liquidity management," Journal of Financial Economics, Elsevier, vol. 124(2), pages 395-414.

    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:hal:journl:hal-02929766. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.