IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v11y2023i4p67-d1109915.html
   My bibliography  Save this article

A Semi-Markov Dynamic Capital Injection Problem for Distressed Banks

Author

Listed:
  • Luca Di Persio

    (Department of Computer Science, College of Mathematics, University of Verona, via Ca’ Vignal 2, 37129 Verona, Italy)

  • Luca Prezioso

    (Department of Mathematics, University of Trento, Via Sommarive, 14, 38123 Trento, Italy)

  • Yilun Jiang

    (Department of Mathematics, The Pennsylvania State University, University Park, State College, PA 16802, USA)

Abstract

Our study investigates the optimal dividend strategy for a bank, taking into account the potential for government capital injections. We explore different types of government interventions, such as liberal, transparent, or uncertain strategies, and consider both single and multiple types of interventions. Our approach differs from others as it focuses on interventions that aim to maintain the overall stability of the financial system, rather than just addressing banks that have already sought government assistance or are in dire need of it. Specifically, we focus on situations where the government is more likely to assist banks that have not requested its intervention or that are not too difficult to save. To accomplish this, we conduct a comprehensive examination of all possible scenarios involving a single, one-time capital injection and derive explicit solutions for the associated optimal control problem. Furthermore, we expand the model to include semi-Markov dynamic capital injection processes and show that the optimal control is the unique viscosity solution of a Hamilton–Jacobi–Bellman equation. The government’s strategy also takes into account the bank’s solvency and any past government interventions.

Suggested Citation

  • Luca Di Persio & Luca Prezioso & Yilun Jiang, 2023. "A Semi-Markov Dynamic Capital Injection Problem for Distressed Banks," Risks, MDPI, vol. 11(4), pages 1-16, March.
    • Handle: RePEc:gam:jrisks:v:11:y:2023:i:4:p:67-:d:1109915
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/11/4/67/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/11/4/67/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hugonnier, Julien & Morellec, Erwan, 2017. "Bank capital, liquid reserves, and insolvency risk," Journal of Financial Economics, Elsevier, vol. 125(2), pages 266-285.
    2. Gerber, Hans U. & Lin, X. Sheldon & Yang, Hailiang, 2006. "A Note on the Dividends-Penalty Identity and the Optimal Dividend Barrier," ASTIN Bulletin, Cambridge University Press, vol. 36(2), pages 489-503, November.
    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. Zhang, Aili & Li, Shuanming & Wang, Wenyuan, 2023. "A scale function based approach for solving integral-differential equations in insurance risk models," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    2. Smaoui, Houcem & Mimouni, Karim & Miniaoui, Héla & Temimi, Akram, 2020. "Funding liquidity risk and banks' risk-taking: Evidence from Islamic and conventional banks," Pacific-Basin Finance Journal, Elsevier, vol. 64(C).
    3. Elmina Homapour & Larry Su & Fabio Caraffini & Francisco Chiclana, 2022. "Regression Analysis of Macroeconomic Conditions and Capital Structures of Publicly Listed British Firms," Mathematics, MDPI, vol. 10(7), pages 1-28, March.
    4. Michi Nishihara & Takashi Shibata, 2020. "Optimal capital structure and bankruptcy cascades," Discussion Papers in Economics and Business 20-10, Osaka University, Graduate School of Economics.
    5. Modena, Andrea, 2020. "Recapitalization, bailout, and long-run welfare in a dynamic model of banking," SAFE Working Paper Series 292, Leibniz Institute for Financial Research SAFE.
    6. Cheung, Eric C.K. & Wong, Jeff T.Y., 2017. "On the dual risk model with Parisian implementation delays in dividend payments," European Journal of Operational Research, Elsevier, vol. 257(1), pages 159-173.
    7. Dung Viet Tran & David McMillan, 2020. "Funding liquidity and bank lending," Cogent Economics & Finance, Taylor & Francis Journals, vol. 8(1), pages 1734324-173, January.
    8. Xie, Jiayi & Zhang, Zhimin, 2020. "Statistical estimation for some dividend problems under the compound Poisson risk model," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 101-115.
    9. Gajek, Lesław & Kuciński, Łukasz, 2017. "Complete discounted cash flow valuation," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 1-19.
    10. Kévin Spinassou & Carole Haritchabalet & Laetitia Lepetit, 2020. "Le ratio de levier comme renforcement des fonds propres : une analyse empirique des conséquences sur le risque et le crédit bancaires," Working Papers hal-02546283, HAL.
    11. Michael Adusei, 2022. "The liquidity risk–financial performance nexus: Evidence from hybrid financial institutions," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 43(1), pages 31-47, January.
    12. Bolton, Patrick & Li, Ye & Wang, Neng & Yang, Jinqiang, 2020. "Dynamic Banking and the Value of Deposits," Working Paper Series 2020-13, Ohio State University, Charles A. Dice Center for Research in Financial Economics.
    13. Leanza, Luca & Sbuelz, Alessandro & Tarelli, Andrea, 2021. "Bail-in vs bail-out: Bank resolution and liability structure," International Review of Financial Analysis, Elsevier, vol. 73(C).
    14. Cheung, Eric C.K. & Landriault, David, 2010. "A generalized penalty function with the maximum surplus prior to ruin in a MAP risk model," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 127-134, February.
    15. Gianni De Nicolò & Nataliya Klimenko & Sebastian Pfeil & Jean-Charles Rochet, 2021. "The Long-Term Effects of Capital Requirements," CESifo Working Paper Series 9115, CESifo.
    16. He, Yue & Kawai, Reiichiro & Shimizu, Yasutaka & Yamazaki, Kazutoshi, 2023. "The Gerber-Shiu discounted penalty function: A review from practical perspectives," Insurance: Mathematics and Economics, Elsevier, vol. 109(C), pages 1-28.
    17. Kulenko, Natalie & Schmidli, Hanspeter, 2008. "Optimal dividend strategies in a Cramér-Lundberg model with capital injections," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 270-278, October.
    18. Zhang, Jinqing & He, Liang & An, Yunbi, 2020. "Measuring banks’ liquidity risk: An option-pricing approach," Journal of Banking & Finance, Elsevier, vol. 111(C).
    19. Thonhauser, Stefan & Albrecher, Hansjorg, 2007. "Dividend maximization under consideration of the time value of ruin," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 163-184, July.
    20. Chadjiconstantinidis, Stathis & Papaioannou, Apostolos D., 2009. "Analysis of the Gerber-Shiu function and dividend barrier problems for a risk process with two classes of claims," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 470-484, December.

    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:gam:jrisks:v:11:y:2023:i:4:p:67-:d:1109915. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.