IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v104y2000i1d10.1023_a1004689008633.html
   My bibliography  Save this article

Optimal Dividend Payout under Compound Poisson Income

Author

Listed:
  • T. Zajic

    (University of Minnesota)

Abstract

We consider an individual who receives income, which may be either positive or negative, and is allowed to pay out a dividend at any time as long as the accumulated income remains positive. In case the accumulated income become negative at some point in time, the individual declares bankruptcy, pays a penalty based on his accumulated income, and the process stops. Assuming that the input process is described by a compound Poisson process and that the individual's value is given by the accumulated dividends minus the penalty, both appropriately discounted, we demonstrate an optimal policy for paying dividends and provide an iterative means for estimating the corresponding value.

Suggested Citation

  • T. Zajic, 2000. "Optimal Dividend Payout under Compound Poisson Income," Journal of Optimization Theory and Applications, Springer, vol. 104(1), pages 195-213, January.
    • Handle: RePEc:spr:joptap:v:104:y:2000:i:1:d:10.1023_a:1004689008633
    DOI: 10.1023/A:1004689008633
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1004689008633
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1004689008633?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. 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.
    2. Asmussen, Soren & Taksar, Michael, 1997. "Controlled diffusion models for optimal dividend pay-out," Insurance: Mathematics and Economics, Elsevier, vol. 20(1), pages 1-15, June.
    3. Hans Gerber & Elias Shiu, 1998. "On the Time Value of Ruin," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 48-72.
    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. Irmina Czarna & Zbigniew Palmowski, 2009. "De Finetti's dividend problem and impulse control for a two-dimensional insurance risk process," Papers 0906.2100, arXiv.org, revised Feb 2011.
    2. Pablo Azcue & Nora Muler & Zbigniew Palmowski, 2016. "Optimal dividend payments for a two-dimensional insurance risk process," Papers 1603.07019, arXiv.org, revised Apr 2018.
    3. F. Avram & Z. Palmowski & M. R. Pistorius, 2011. "On Gerber-Shiu functions and optimal dividend distribution for a L\'{e}vy risk process in the presence of a penalty function," Papers 1110.4965, arXiv.org, revised Jun 2015.
    4. Yongwu Li & Zhongfei Li & Yan Zeng, 2016. "Equilibrium Dividend Strategy with Non-exponential Discounting in a Dual Model," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 699-722, February.

    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. Jukka Isohätälä & Alistair Milne & Donald Robertson, 2020. "The Net Worth Trap: Investment and Output Dynamics in the Presence of Financing Constraints," Mathematics, MDPI, vol. 8(8), pages 1-32, August.
    2. Meng, Hui & Siu, Tak Kuen, 2011. "On optimal reinsurance, dividend and reinvestment strategies," Economic Modelling, Elsevier, vol. 28(1-2), pages 211-218, January.
    3. 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.
    4. Szölgyenyi Michaela, 2015. "Dividend maximization in a hidden Markov switching model," Statistics & Risk Modeling, De Gruyter, vol. 32(3-4), pages 143-158, December.
    5. Runhuan Feng & Hans Volkmer & Shuaiqi Zhang & Chao Zhu, 2011. "Optimal Dividend Payments for the Piecewise-Deterministic Poisson Risk Model," Papers 1106.2781, arXiv.org, revised Nov 2014.
    6. He, Lin & Liang, Zongxia, 2008. "Optimal financing and dividend control of the insurance company with proportional reinsurance policy," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 976-983, June.
    7. Yuen, Kam C. & Wang, Guojing & Li, Wai K., 2007. "The Gerber-Shiu expected discounted penalty function for risk processes with interest and a constant dividend barrier," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 104-112, January.
    8. Ernst, Philip A. & Imerman, Michael B. & Shepp, Larry & Zhou, Quan, 2022. "Fiscal stimulus as an optimal control problem," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 1091-1108.
    9. Hansjörg Albrecher & Pablo Azcue & Nora Muler, 2023. "Optimal dividends under a drawdown constraint and a curious square-root rule," Finance and Stochastics, Springer, vol. 27(2), pages 341-400, April.
    10. Gunther Leobacher & Michaela Szolgyenyi & Stefan Thonhauser, 2016. "Bayesian Dividend Optimization and Finite Time Ruin Probabilities," Papers 1602.04660, arXiv.org.
    11. 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.
    12. Liu, Zhang & Chen, Ping & Hu, Yijun, 2020. "On the dual risk model with diffusion under a mixed dividend strategy," Applied Mathematics and Computation, Elsevier, vol. 376(C).
    13. 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.
    14. Meng, Hui & Siu, Tak Kuen & Yang, Hailiang, 2013. "Optimal dividends with debts and nonlinear insurance risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 110-121.
    15. Sotomayor, Luz R. & Cadenillas, Abel, 2011. "Classical and singular stochastic control for the optimal dividend policy when there is regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 344-354, May.
    16. Larsson, Bo & Wijkander, Hans, 2019. "Banking, Capital Regulation, Risk and Dynamics," Research Papers in Economics 2019:4, Stockholm University, Department of Economics.
    17. Albrecher, Hansjörg & Bäuerle, Nicole & Bladt, Martin, 2018. "Dividends: From refracting to ratcheting," Insurance: Mathematics and Economics, Elsevier, vol. 83(C), pages 47-58.
    18. Stefan Kremsner & Alexander Steinicke & Michaela Szolgyenyi, 2020. "A deep neural network algorithm for semilinear elliptic PDEs with applications in insurance mathematics," Papers 2010.15757, arXiv.org, revised Dec 2020.
    19. Igor G. Pospelov & Stanislav A. Radionov, 2015. "Optimal Dividend Policy When Cash Surplus Follows The Telegraph Process," HSE Working papers WP BRP 48/FE/2015, National Research University Higher School of Economics.
    20. Michaela Szolgyenyi, 2016. "Dividend maximization in a hidden Markov switching model," Papers 1602.04656, arXiv.org.

    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:spr:joptap:v:104:y:2000:i:1:d:10.1023_a:1004689008633. 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.