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Systemic robustness: a mean-field particle system approach

Author

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  • Erhan Bayraktar
  • Gaoyue Guo
  • Wenpin Tang
  • Yuming Paul Zhang

Abstract

This paper is concerned with the problem of budget control in a large particle system modeled by stochastic differential equations involving hitting times, which arises from considerations of systemic risk in a regional financial network. Motivated by Tang and Tsai (Ann. Probab., 46(2018), pp. 1597{1650), we focus on the number or proportion of surviving entities that never default to measure the systemic robustness. First we show that both the mean-field particle system and its limiting McKean-Vlasov equation are well-posed by virtue of the notion of minimal solutions. We then establish a connection between the proportion of surviving entities in the large particle system and the probability of default in the limiting McKean-Vlasov equation as the size of the interacting particle system N tends to infinity. Finally, we study the asymptotic efficiency of budget control in different economy regimes: the expected number of surviving entities is of constant order in a negative economy; it is of order of the square root of N in a neutral economy; and it is of order N in a positive economy where the budget's effect is negligible.

Suggested Citation

  • Erhan Bayraktar & Gaoyue Guo & Wenpin Tang & Yuming Paul Zhang, 2022. "Systemic robustness: a mean-field particle system approach," Papers 2212.08518, arXiv.org, revised Aug 2023.
    • Handle: RePEc:arx:papers:2212.08518
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    References listed on IDEAS

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    4. Glasserman, Paul & Young, H. Peyton, 2016. "Contagion in financial networks," LSE Research Online Documents on Economics 68681, London School of Economics and Political Science, LSE Library.
    5. Paul Glasserman & H. Peyton Young, 2016. "Contagion in Financial Networks," Journal of Economic Literature, American Economic Association, vol. 54(3), pages 779-831, September.
    6. Kay Giesecke & Konstantinos Spiliopoulos & Richard B. Sowers & Justin A. Sirignano, 2011. "Large Portfolio Asymptotics for Loss From Default," Papers 1109.1272, arXiv.org, revised Feb 2015.
    7. Delarue, F. & Inglis, J. & Rubenthaler, S. & Tanré, E., 2015. "Particle systems with a singular mean-field self-excitation. Application to neuronal networks," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2451-2492.
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    Cited by:

    1. Mao Fabrice Djete & Gaoyue Guo & Nizar Touzi, 2023. "Mean field game of mutual holding with defaultable agents, and systemic risk," Papers 2303.07996, arXiv.org.

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