IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v179y2018i2d10.1007_s10957-017-1185-1.html
   My bibliography  Save this article

Systemic Risk and Interbank Lending

Author

Listed:
  • Li-Hsien Sun

    (National Central University)

Abstract

We propose a simple model of the banking system incorporating a game feature, where the evolution of monetary reserve is modeled as a system of coupled Feller diffusions. The optimization reflects the desire of each bank to borrow from or lend to a central bank through manipulating its lending preference and the intention of each bank to deposit in the central bank in order to control the reserve and the corresponding volatility for cost minimization. The Markov Nash equilibrium for finite many players generated by minimizing the linear quadratic cost subject to Cox–Ingersoll–Ross type processes creates liquidity and deposit rate. The adding liquidity leads to a flocking effect implying stability or systemic risk depending on the level of the growth rate, but the deposit rate diminishes the growth of the total monetary reserve causing a large number of bank defaults. The central bank acts as a central deposit corporation. In addition, the corresponding mean field game in the case of the number of banks N large and the infinite time horizon stochastic game with the discount factor are also discussed.

Suggested Citation

  • Li-Hsien Sun, 2018. "Systemic Risk and Interbank Lending," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 400-424, November.
    • Handle: RePEc:spr:joptap:v:179:y:2018:i:2:d:10.1007_s10957-017-1185-1
    DOI: 10.1007/s10957-017-1185-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-017-1185-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-017-1185-1?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. A. Bensoussan & K. C. J. Sung & S. C. P. Yam & S. P. Yung, 2016. "Linear-Quadratic Mean Field Games," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 496-529, May.
    2. Rene Carmona & Jean-Pierre Fouque & Seyyed Mostafa Mousavi & Li-Hsien Sun, 2016. "Systemic Risk and Stochastic Games with Delay," Papers 1607.06373, arXiv.org.
    3. Gilles-Edouard Espinosa & Nizar Touzi, 2015. "Optimal Investment Under Relative Performance Concerns," Mathematical Finance, Wiley Blackwell, vol. 25(2), pages 221-257, April.
    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. Tomoyuki Ichiba & Michael Ludkovski & Andrey Sarantsev, 2019. "Dynamic contagion in a banking system with births and defaults," Annals of Finance, Springer, vol. 15(4), pages 489-538, December.
    2. Zachary Feinstein & Andreas Sojmark, 2019. "A Dynamic Default Contagion Model: From Eisenberg-Noe to the Mean Field," Papers 1912.08695, arXiv.org.
    3. Rama Cont & Xin Guo & Renyuan Xu, 2020. "Pareto Optima for a Class of Singular Control Games," Working Papers hal-03049246, HAL.
    4. Lorella Fatone & Francesca Mariani, 2020. "Systemic risk governance in a dynamical model of a banking system with stochastic assets and liabilities," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 15(1), pages 183-219, January.
    5. Chotipong Charoensom & Thaisiri Watewai, 2022. "Optimal Liquidity Control and Systemic Risk in an Interbank Network with Liquidity Shocks and Regime-dependent Interconnectedness," PIER Discussion Papers 175, Puey Ungphakorn Institute for Economic Research.
    6. Yu-Jui Huang & Li-Hsien Sun, 2023. "Partial Information Breeds Systemic Risk," Papers 2312.04045, arXiv.org, revised Dec 2023.
    7. Doumpos, Michalis & Zopounidis, Constantin & Gounopoulos, Dimitrios & Platanakis, Emmanouil & Zhang, Wenke, 2023. "Operational research and artificial intelligence methods in banking," European Journal of Operational Research, Elsevier, vol. 306(1), pages 1-16.
    8. Lijun Bo & Tongqing Li & Xiang Yu, 2021. "Centralized systemic risk control in the interbank system: Weak formulation and Gamma-convergence," Papers 2106.09978, arXiv.org, revised May 2022.
    9. Li-Hsien Sun, 2022. "Mean Field Games with Heterogeneous Groups: Application to Banking Systems," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 130-167, January.
    10. Aditya Maheshwari & Andrey Sarantsev, 2018. "Modeling Financial System with Interbank Flows, Borrowing, and Investing," Risks, MDPI, vol. 6(4), pages 1-26, November.
    11. Rama Cont & Xin Guo & Renyuan Xu, 2021. "Interbank lending with benchmark rates: Pareto optima for a class of singular control games," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1357-1393, October.
    12. Bo, Lijun & Li, Tongqing & Yu, Xiang, 2022. "Centralized systemic risk control in the interbank system: Weak formulation and Gamma-convergence," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 622-654.
    13. Tabak, Benjamin Miranda & Silva, Thiago Christiano & Fiche, Marcelo Estrela & Braz, Tércio, 2021. "Citation likelihood analysis of the interbank financial networks literature: A machine learning and bibliometric approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 562(C).

    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. Han, Jinhui & Ma, Guiyuan & Yam, Sheung Chi Phillip, 2022. "Relative performance evaluation for dynamic contracts in a large competitive market," European Journal of Operational Research, Elsevier, vol. 302(2), pages 768-780.
    2. Li-Hsien Sun, 2022. "Mean Field Games with Heterogeneous Groups: Application to Banking Systems," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 130-167, January.
    3. Daniel Lacker & Thaleia Zariphopoulou, 2017. "Mean field and n-agent games for optimal investment under relative performance criteria," Papers 1703.07685, arXiv.org, revised Jun 2018.
    4. Li-Hsien Sun, 2019. "Systemic Risk and Heterogeneous Mean Field Type Interbank Network," Papers 1907.03082, arXiv.org, revised Sep 2019.
    5. Shuenn-Jyi Sheu & Li-Hsien Sun & Zheng Zhang, 2018. "Portfolio Optimization with Delay Factor Models," Papers 1805.01118, arXiv.org.
    6. Curatola, Giuliano, 2022. "Price impact, strategic interaction and portfolio choice," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    7. Francesca Biagini & Andrea Mazzon & Thilo Meyer-Brandis, 2018. "Financial asset bubbles in banking networks," Papers 1806.01728, arXiv.org.
    8. Aditya Maheshwari & Andrey Sarantsev, 2017. "Modeling Financial System with Interbank Flows, Borrowing, and Investing," Papers 1707.03542, arXiv.org, revised Oct 2018.
    9. Asmussen, Søren & Christensen, Bent Jesper & Thøgersen, Julie, 2019. "Nash equilibrium premium strategies for push–pull competition in a frictional non-life insurance market," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 92-100.
    10. Ludovic Tangpi & Shichun Wang, 2022. "Optimal Bubble Riding: A Mean Field Game with Varying Entry Times," Papers 2209.04001, arXiv.org, revised Jan 2024.
    11. Jana Bielagk & Arnaud Lionnet & Gonçalo dos Reis, 2015. "Equilibrium pricing under relative performance concerns," Working Papers hal-01245812, HAL.
    12. Haoyang Cao & Jodi Dianetti & Giorgio Ferrari, 2021. "Stationary Discounted and Ergodic Mean Field Games of Singular Control," Papers 2105.07213, arXiv.org.
    13. Masaaki Fujii & Masashi Sekine, 2023. "Mean-field Equilibrium Price Formation with Exponential Utility," CIRJE F-Series CIRJE-F-1210, CIRJE, Faculty of Economics, University of Tokyo.
    14. Wang, Ning & Zhang, Nan & Jin, Zhuo & Qian, Linyi, 2021. "Stochastic differential investment and reinsurance games with nonlinear risk processes and VaR constraints," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 168-184.
    15. Zongxia Liang & Keyu Zhang, 2023. "Time-inconsistent mean field and n-agent games under relative performance criteria," Papers 2312.14437, arXiv.org.
    16. Kim Weston, 2022. "Existence of an equilibrium with limited participation," Papers 2206.12399, arXiv.org.
    17. Zhu, Huainian & Cao, Ming & Zhang, Chengke, 2019. "Time-consistent investment and reinsurance strategies for mean-variance insurers with relative performance concerns under the Heston model," Finance Research Letters, Elsevier, vol. 30(C), pages 280-291.
    18. Shuzhen Yang, 2020. "Bellman type strategy for the continuous time mean-variance model," Papers 2005.01904, arXiv.org, revised Jul 2020.
    19. Guanxing Fu, 2022. "Mean Field Portfolio Games with Consumption," Papers 2206.05425, arXiv.org, revised Dec 2022.
    20. Yongxin Chen & Tryphon T. Georgiou & Michele Pavon, 2018. "Steering the Distribution of Agents in Mean-Field Games System," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 332-357, October.

    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:179:y:2018:i:2:d:10.1007_s10957-017-1185-1. 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.