IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1602.04656.html
   My bibliography  Save this paper

Dividend maximization in a hidden Markov switching model

Author

Listed:
  • Michaela Szolgyenyi

Abstract

In this paper we study the valuation problem of an insurance company by maximizing the expected discounted future dividend payments in a model with partial information that allows for a changing economic environment. The surplus process is modeled as a Brownian motion with drift. This drift depends on an underlying Markov chain the current state of which is assumed to be unobservable. The different states of the Markov chain thereby represent different phases of the economy. We apply results from filtering theory to overcome uncertainty and then we give an analytic characterization of the optimal value function. Finally, we present a numerical study covering various scenarios to get a clear picture of how dividends should be paid out.

Suggested Citation

  • Michaela Szolgyenyi, 2016. "Dividend maximization in a hidden Markov switching model," Papers 1602.04656, arXiv.org.
  • Handle: RePEc:arx:papers:1602.04656
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1602.04656
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Rudiger Frey & Abdelali Gabih & Ralf Wunderlich, 2013. "Portfolio Optimization under Partial Information with Expert Opinions: a Dynamic Programming Approach," Papers 1303.2513, arXiv.org, revised Feb 2014.
    2. Rüdiger Frey & Abdelali Gabih & Ralf Wunderlich, 2012. "Portfolio Optimization Under Partial Information With Expert Opinions," World Scientific Book Chapters, in: Matheus R Grasselli & Lane P Hughston (ed.), Finance at Fields, chapter 11, pages 265-282, World Scientific Publishing Co. Pte. Ltd..
    3. Zhu, Jinxia & Chen, Feng, 2013. "Dividend optimization for regime-switching general diffusions," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 439-456.
    4. 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.
    5. Benjamin Avanzi, 2009. "Strategies for Dividend Distribution: A Review," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(2), pages 217-251.
    6. Décamps, Jean-Paul & Villeneuve, Stéphane, 2015. "Integrating profitability prospects and cash management," IDEI Working Papers 849, Institut d'Économie Industrielle (IDEI), Toulouse.
    7. Hubalek, Friedrich & Schachermayer, Walter, 2004. "Optimizing expected utility of dividend payments for a Brownian risk process and a peculiar nonlinear ODE," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 193-225, April.
    8. 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.
    9. 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.
    10. Gerber, Hans U., 1977. "On Optimal Cancellation of Policies," ASTIN Bulletin, Cambridge University Press, vol. 9(1-2), pages 125-138, January.
    11. Jörn Sass & Ulrich Haussmann, 2004. "Optimizing the terminal wealth under partial information: The drift process as a continuous time Markov chain," Finance and Stochastics, Springer, vol. 8(4), pages 553-577, November.
    12. Liang, Zhibin & Bayraktar, Erhan, 2014. "Optimal reinsurance and investment with unobservable claim size and intensity," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 156-166.
    13. Rüdiger Frey & Abdelali Gabih & Ralf Wunderlich, 2012. "Portfolio Optimization Under Partial Information With Expert Opinions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-18.
    14. 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)

    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. Szölgyenyi Michaela, 2015. "Dividend maximization in a hidden Markov switching model," Statistics & Risk Modeling, De Gruyter, vol. 32(3-4), pages 143-158, December.
    2. Gunther Leobacher & Michaela Szolgyenyi & Stefan Thonhauser, 2016. "Bayesian Dividend Optimization and Finite Time Ruin Probabilities," Papers 1602.04660, arXiv.org.
    3. 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.
    4. 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.
    5. Abdelali Gabih & Hakam Kondakji & Jorn Sass & Ralf Wunderlich, 2014. "Expert Opinions and Logarithmic Utility Maximization in a Market with Gaussian Drift," Papers 1402.6313, arXiv.org.
    6. Christoph Knochenhauer & Alexander Merkel & Yufei Zhang, 2024. "Optimal Investment with Costly Expert Opinions," Papers 2409.11569, arXiv.org.
    7. Jörn Sass & Dorothee Westphal & Ralf Wunderlich, 2017. "Expert Opinions And Logarithmic Utility Maximization For Multivariate Stock Returns With Gaussian Drift," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(04), pages 1-41, June.
    8. Abdelali Gabih & Hakam Kondakji & Ralf Wunderlich, 2018. "Asymptotic Filter Behavior for High-Frequency Expert Opinions in a Market with Gaussian Drift," Papers 1812.03453, arXiv.org, revised Mar 2020.
    9. Jorn Sass & Dorothee Westphal & Ralf Wunderlich, 2016. "Expert Opinions and Logarithmic Utility Maximization for Multivariate Stock Returns with Gaussian Drift," Papers 1601.08155, arXiv.org, revised Mar 2016.
    10. Abdelali Gabih & Hakam Kondakji & Ralf Wunderlich, 2023. "Power Utility Maximization with Expert Opinions at Fixed Arrival Times in a Market with Hidden Gaussian Drift," Papers 2301.06847, arXiv.org, revised Jun 2024.
    11. Abdelali Gabih & Hakam Kondakji & Ralf Wunderlich, 2022. "Well Posedness of Utility Maximization Problems Under Partial Information in a Market with Gaussian Drift," Papers 2205.08614, arXiv.org, revised Jul 2024.
    12. 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.
    13. Abdelali Gabih & Hakam Kondakji & Ralf Wunderlich, 2024. "Power utility maximization with expert opinions at fixed arrival times in a market with hidden Gaussian drift," Annals of Operations Research, Springer, vol. 341(2), pages 897-936, October.
    14. 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.
    15. Tiziano Angelis, 2020. "Optimal dividends with partial information and stopping of a degenerate reflecting diffusion," Finance and Stochastics, Springer, vol. 24(1), pages 71-123, January.
    16. Giorgio Ferrari & Patrick Schuhmann & Shihao Zhu, 2021. "Optimal Dividends under Markov-Modulated Bankruptcy Level," Papers 2111.03724, arXiv.org, revised Jun 2022.
    17. 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.
    18. Abdelali Gabih & Ralf Wunderlich, 2023. "Portfolio Optimization in a Market with Hidden Gaussian Drift and Randomly Arriving Expert Opinions: Modeling and Theoretical Results," Papers 2308.02049, arXiv.org, revised Jun 2024.
    19. Jiang, Zhengjun, 2019. "Optimal dividend policy when risk reserves follow a jump–diffusion process with a completely monotone jump density under Markov-regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 1-7.
    20. Julia Eisenberg & Paul Kruhner, 2018. "Suboptimal Control of Dividends under Exponential Utility," Papers 1809.01983, arXiv.org, revised Jan 2019.

    More about this item

    Statistics

    Access and download statistics

    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:arx:papers:1602.04656. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.