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Banks as Tanks: A Continuous-Time Model of Financial Clearing

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  • Isaac M. Sonin
  • Konstantin Sonin

Abstract

We present a simple continuous-time model of clearing in financial networks. Financial firms are represented as "tanks" filled with fluid (money), flowing in and out. Once "pipes" connecting "tanks" are open, the system reaches the clearing payment vector in finite time. This approach provides a simple recursive solution to a classical static model of financial clearing in bankruptcy, and suggests a practical payment mechanism. With sufficient resources, a system of mutual obligations can be restructured into an equivalent system that has a cascade structure: there is a group of banks that paid off their debts, another group that owes money only to banks in the first group, and so on. Technically, we use the machinery of Markov chains to analyze evolution of a deterministic dynamical system.

Suggested Citation

  • Isaac M. Sonin & Konstantin Sonin, 2017. "Banks as Tanks: A Continuous-Time Model of Financial Clearing," Papers 1705.05943, arXiv.org, revised Jul 2020.
    • Handle: RePEc:arx:papers:1705.05943
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    References listed on IDEAS

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    1. Yuri Kabanov & Robert Liptser, 2006. "From Stochastic Calculus to Mathematical Finance. The Shiryaev Festschrift," Post-Print hal-00488295, HAL.
    2. Janet L. Yellen, 2013. "Interconnectedness and Systemic Risk: Lessons from the Financial Crisis and Policy Implications : a speech at the American Economic Association/American Finance Association Joint Luncheon, San Diego, ," Speech 631, Board of Governors of the Federal Reserve System (U.S.).
    3. Daron Acemoglu & Asuman Ozdaglar & Alireza Tahbaz-Salehi, 2015. "Systemic Risk and Stability in Financial Networks," American Economic Review, American Economic Association, vol. 105(2), pages 564-608, February.
    4. Sonin, Isaac M., 2008. "A generalized Gittins index for a Markov chain and its recursive calculation," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1526-1533, September.
    5. Larry Eisenberg & Thomas H. Noe, 2001. "Systemic Risk in Financial Systems," Management Science, INFORMS, vol. 47(2), pages 236-249, February.
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    Cited by:

    1. Feinstein, Zachary & Sojmark, Andreas, 2021. "Short communication: dynamic default contagion in heterogeneous interbank systems," LSE Research Online Documents on Economics 123789, London School of Economics and Political Science, LSE Library.
    2. Zachary Feinstein & Andreas Sojmark, 2019. "A Dynamic Default Contagion Model: From Eisenberg-Noe to the Mean Field," Papers 1912.08695, arXiv.org.
    3. Zachary Feinstein & Andreas Sojmark, 2020. "Dynamic Default Contagion in Heterogeneous Interbank Systems," Papers 2010.15254, arXiv.org, revised Jul 2021.
    4. Matteo Citterio & Marco D'Errico & Gabriele Visentin, 2024. "Conditional Forecasting of Margin Calls using Dynamic Graph Neural Networks," Papers 2410.23275, arXiv.org.
    5. Banerjee, Tathagata & Bernstein, Alex & Feinstein, Zachary, 2025. "Dynamic clearing and contagion in financial networks," European Journal of Operational Research, Elsevier, vol. 321(2), pages 664-675.
    6. Hong Chen & Tan Wang & David D. Yao, 2021. "Financial Network and Systemic Risk—A Dynamic Model," Production and Operations Management, Production and Operations Management Society, vol. 30(8), pages 2441-2466, August.
    7. Zhiyu Cao & Zachary Feinstein, 2025. "Price-mediated contagion with endogenous market liquidity," Mathematics and Financial Economics, Springer, volume 19, number 4, December.
    8. Zhiyu Cao & Zachary Feinstein, 2023. "Price-mediated contagion with endogenous market liquidity," Papers 2311.05977, arXiv.org, revised Sep 2024.

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