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. 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).
    2. 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.
    3. Dung Viet Tran & David McMillan, 2020. "Funding liquidity and bank lending," Cogent Economics & Finance, Taylor & Francis Journals, vol. 8(1), pages 1734324-173, January.
    4. 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).
    5. 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.
    6. 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.
    7. 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.
    8. Zhang, Jinqing & He, Liang & An, Yunbi, 2020. "Measuring banks’ liquidity risk: An option-pricing approach," Journal of Banking & Finance, Elsevier, vol. 111(C).
    9. 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.
    10. 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.
    11. Nishihara, Michi & Shibata, Takashi, 2021. "Optimal capital structure and simultaneous bankruptcy of firms in corporate networks," Journal of Economic Dynamics and Control, Elsevier, vol. 133(C).
    12. Hugonnier, Julien & Morellec, Erwan, 2017. "Bank capital, liquid reserves, and insolvency risk," Journal of Financial Economics, Elsevier, vol. 125(2), pages 266-285.
    13. Zhao, Zhiming & Li, Shasha & Tang, Huiling, 2021. "Write-down bonds, credit risk and imperfect information," The North American Journal of Economics and Finance, Elsevier, vol. 57(C).
    14. Paseda, Oluseun & Olowe, Rufus, 2018. "The Debt Maturity Structure of Nigerian Quoted Firms," MPRA Paper 117061, University Library of Munich, Germany, revised 30 Jun 2018.
    15. Biffis, Enrico & Kyprianou, Andreas E., 2010. "A note on scale functions and the time value of ruin for Lévy insurance risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 85-91, February.
    16. Huang, Chao & Moreira, Fernando & Archibald, Thomas W., 2024. "Should Basel-style liquidity requirements be set countercyclically? Evidence from a numerical analysis," International Review of Financial Analysis, Elsevier, vol. 95(PB).
    17. 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.
    18. Ripamonti, Alexandre, 2020. "Financial institutions, asymmetric information and capital structure adjustments," The Quarterly Review of Economics and Finance, Elsevier, vol. 77(C), pages 75-83.
    19. 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.
    20. Wang, Chih-Wei & Lee, Chien-Chiang & Chen, Ming-Chien, 2022. "The effects of economic policy uncertainty and country governance on banks' liquidity creation: International evidence," Pacific-Basin Finance Journal, Elsevier, vol. 71(C).

    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.