IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v150y2022icp622-654.html
   My bibliography  Save this article

Centralized systemic risk control in the interbank system: Weak formulation and Gamma-convergence

Author

Listed:
  • Bo, Lijun
  • Li, Tongqing
  • Yu, Xiang

Abstract

This paper studies a systemic risk control problem by the central bank, which dynamically plans monetary supply to stabilize the interbank system with borrowing and lending activities. Facing both heterogeneity among banks and the common noise, the central bank aims to find an optimal strategy to minimize the average distance between log-monetary reserves of all banks and the benchmark of some target steady levels. A weak formulation is adopted, and an optimal randomized control can be obtained in the system with finite banks by applying Ekeland’s variational principle. As the number of banks grows large, we prove the convergence of optimal strategies using the Gamma-convergence argument, which yields an optimal weak control in the mean field model. It is shown that this mean field optimal control is associated to the solution of a stochastic Fokker–Planck–Kolmogorov (FPK) equation, for which the uniqueness of the solution is established under some mild conditions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:150:y:2022:i:c:p:622-654
    DOI: 10.1016/j.spa.2022.05.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414922001193
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2022.05.005?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. Alan S. Blinder & Michael Ehrmann & Marcel Fratzscher & Jakob De Haan & David-Jan Jansen, 2008. "Central Bank Communication and Monetary Policy: A Survey of Theory and Evidence," Journal of Economic Literature, American Economic Association, vol. 46(4), pages 910-945, December.
    2. Kurtz, Thomas G. & Xiong, Jie, 1999. "Particle representations for a class of nonlinear SPDEs," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 103-126, September.
    3. Mr. Simon T Gray, 2011. "Central Bank Balances and Reserve Requirements," IMF Working Papers 2011/036, International Monetary Fund.
    4. Lorella Fatone & Francesca Mariani, 2019. "An assets-liabilities dynamical model of banking system and systemic risk governance," Papers 1905.12431, arXiv.org.
    5. Alan S. Blinder & Michael Ehrmann & Marcel Fratzscher & Jakob De Haan & David-Jan Jansen, 2008. "Central Bank Communication and Monetary Policy: A Survey of Theory and Evidence," Journal of Economic Literature, American Economic Association, vol. 46(4), pages 910-945, December.
    6. repec:pri:cepsud:161blinder is not listed on IDEAS
    7. Joyce, Michael, 2012. "Quantitative easing and other unconventional monetary policies: Bank of England conference summary," Bank of England Quarterly Bulletin, Bank of England, vol. 52(1), pages 48-56.
    8. Michael Joyce & David Miles & Andrew Scott & Dimitri Vayanos, 2012. "Quantitative Easing and Unconventional Monetary Policy – an Introduction," Economic Journal, Royal Economic Society, vol. 122(564), pages 271-288, November.
    9. Lijun Bo & Huafu Liao & Xiang Yu, 2020. "Optimal Tracking Portfolio with A Ratcheting Capital Benchmark," Papers 2006.13661, arXiv.org, revised Apr 2021.
    10. 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.
    11. Agostino Capponi & Xu Sun & David D. Yao, 2020. "A Dynamic Network Model of Interbank Lending—Systemic Risk and Liquidity Provisioning," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 1127-1152, August.
    12. Chang, Chun & Liu, Zheng & Spiegel, Mark M. & Zhang, Jingyi, 2019. "Reserve requirements and optimal Chinese stabilization policy," Journal of Monetary Economics, Elsevier, vol. 103(C), pages 33-51.
    13. Lorella Fatone & Francesca Mariani, 2019. "Systemic risk governance in a dynamical model of a banking system," Journal of Global Optimization, Springer, vol. 75(3), pages 851-883, November.
    14. Li-Hsien Sun, 2018. "Systemic Risk and Interbank Lending," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 400-424, 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. 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.
    2. Collingro, Franziska & Frenkel, Michael, 2020. "On the financial market impact of euro area monetary policy: A comparative study before and after the Global Financial Crisis," Global Finance Journal, Elsevier, vol. 45(C).
    3. Falagiarda, Matteo & Reitz, Stefan, 2015. "Announcements of ECB unconventional programs: Implications for the sovereign spreads of stressed euro area countries," Journal of International Money and Finance, Elsevier, vol. 53(C), pages 276-295.
    4. Green, Christopher & Bai, Ye & Murinde, Victor & Ngoka, Kethi & Maana, Isaya & Tiriongo, Samuel, 2016. "Overnight interbank markets and the determination of the interbank rate: A selective survey," International Review of Financial Analysis, Elsevier, vol. 44(C), pages 149-161.
    5. 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.
    6. Falagiarda, Matteo & Reitz, Stefan, 2013. "Announcements of ECB unconventional programs: Implications for the sovereign risk of Italy," Kiel Working Papers 1866, Kiel Institute for the World Economy (IfW Kiel).
    7. Tadle, Raul Cruz, 2022. "FOMC minutes sentiments and their impact on financial markets," Journal of Economics and Business, Elsevier, vol. 118(C).
    8. Anastasios Evgenidis & Stephanos Papadamou, 2021. "The impact of unconventional monetary policy in the euro area. Structural and scenario analysis from a Bayesian VAR," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(4), pages 5684-5703, October.
    9. Taiga Saito & Akihiko Takahashi, 2019. "A novel approach to asset pricing with choice of probability measures," CARF F-Series CARF-F-471, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo, revised Jan 2021.
    10. Benjamin Born & Michael Ehrmann & Marcel Fratzscher, 2011. "How Should Central Banks Deal with a Financial Stability Objective? The Evolving Role of Communication as a Policy Instrument," Chapters, in: Sylvester Eijffinger & Donato Masciandaro (ed.), Handbook of Central Banking, Financial Regulation and Supervision, chapter 9, Edward Elgar Publishing.
    11. Michael Pedersen, 2020. "Surveying the survey: What can we learn about the effects of monetary policy on inflation expectations?," Working Papers Central Bank of Chile 889, Central Bank of Chile.
    12. Yoshito Funashima, 2022. "Economic policy uncertainty and unconventional monetary policy," Manchester School, University of Manchester, vol. 90(3), pages 278-292, June.
    13. Jonne Lehtimäki & Marianne Palmu, 2022. "Who Should You Listen to in a Crisis? Differences in Communication of Central Bank Policymakers," Journal of Central Banking Theory and Practice, Central bank of Montenegro, vol. 11(3), pages 33-57.
    14. Marins, Jaqueline Terra Moura & Vicente, José Valentim Machado, 2017. "Do the central bank actions reduce interest rate volatility?," Economic Modelling, Elsevier, vol. 65(C), pages 129-137.
    15. Lloyd, S. P., 2017. "Unconventional Monetary Policy and the Interest Rate Channel: Signalling and Portfolio Rebalancing," Cambridge Working Papers in Economics 1735, Faculty of Economics, University of Cambridge.
    16. Fischer, Andreas M. & Ranaldo, Angelo, 2011. "Does FOMC news increase global FX trading?," Journal of Banking & Finance, Elsevier, vol. 35(11), pages 2965-2973, November.
    17. Josh Ryan-Collins, 2015. "Is Monetary Financing Inflationary? A Case Study of the Canadian Economy, 1935-75," Economics Working Paper Archive wp_848, Levy Economics Institute.
    18. Diaconescu Diana Raluca & Botezatu Hortensia Paula, 2015. "National Bank Of Romania Monetary Policy Transmission Mechanism During The Crisis," Annals - Economy Series, Constantin Brancusi University, Faculty of Economics, vol. 2, pages 327-333, April.
    19. Claus Brand & Daniel Buncic & Jarkko Turunen, 2010. "The Impact of ECB Monetary Policy Decisions and Communication on the Yield Curve," Journal of the European Economic Association, MIT Press, vol. 8(6), pages 1266-1298, December.
    20. Jonathan G James & Phillip Lawler, 2017. "Optimal Transparency and Policy Intervention with Heterogeneous Signals and Information Stickiness," Manchester School, University of Manchester, vol. 85(5), pages 577-600, September.

    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:eee:spapps:v:150:y:2022:i:c:p:622-654. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    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.