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Systemic risk in a mean-field model of interbank lending with self-exciting shocks

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  • Anastasia Borovykh
  • Andrea Pascucci
  • Stefano la Rovere

Abstract

In this paper we consider a mean-field model of interacting diffusions for the monetary reserves in which the reserves are subjected to a self- and cross-exciting shock. This is motivated by the financial acceleration and fire sales observed in the market. We derive a mean-field limit using a weak convergence analysis and find an explicit measure-valued process associated with a large interbanking system. We define systemic risk indicators and derive, using the limiting process, several law of large numbers results and verify these numerically. We conclude that self-exciting shocks increase the systemic risk in the network and their presence in interbank networks should not be ignored.

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  • Anastasia Borovykh & Andrea Pascucci & Stefano la Rovere, 2017. "Systemic risk in a mean-field model of interbank lending with self-exciting shocks," Papers 1710.00231, arXiv.org, revised Jun 2018.
    • Handle: RePEc:arx:papers:1710.00231
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    Cited by:

    1. 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.
    2. Zachary Feinstein & Andreas Sojmark, 2019. "A Dynamic Default Contagion Model: From Eisenberg-Noe to the Mean Field," Papers 1912.08695, arXiv.org.
    3. Yaguang Wu & Qingan Qiu, 2022. "Optimal Triggering Policy of Protective Devices Considering Self-Exciting Mechanism of Shocks," Mathematics, MDPI, vol. 10(15), pages 1-18, August.
    4. Morteza Alaeddini & Philippe Madiès & Paul J. Reaidy & Julie Dugdale, 2023. "Interbank money market concerns and actors’ strategies—A systematic review of 21st century literature," Journal of Economic Surveys, Wiley Blackwell, vol. 37(2), pages 573-654, April.
    5. Sebastian Jaimungal, 2022. "Reinforcement learning and stochastic optimisation," Finance and Stochastics, Springer, vol. 26(1), pages 103-129, January.

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