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Large deviations for a mean field model of systemic risk

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  • Josselin Garnier
  • George Papanicolaou
  • Tzu-Wei Yang

Abstract

We consider a system of diffusion processes that interact through their empirical mean and have a stabilizing force acting on each of them, corresponding to a bistable potential. There are three parameters that characterize the system: the strength of the intrinsic stabilization, the strength of the external random perturbations, and the degree of cooperation or interaction between them. The latter is the rate of mean reversion of each component to the empirical mean of the system. We interpret this model in the context of systemic risk and analyze in detail the effect of cooperation between the components, that is, the rate of mean reversion. We show that in a certain regime of parameters increasing cooperation tends to increase the stability of the individual agents but it also increases the overall or systemic risk. We use the theory of large deviations of diffusions interacting through their mean field.

Suggested Citation

  • Josselin Garnier & George Papanicolaou & Tzu-Wei Yang, 2012. "Large deviations for a mean field model of systemic risk," Papers 1204.3536, arXiv.org, revised Aug 2012.
    • Handle: RePEc:arx:papers:1204.3536
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    References listed on IDEAS

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    1. Gai, Prasanna & Kapadia, Sujit, 2010. "Contagion in financial networks," Bank of England working papers 383, Bank of England.
    2. J. Lorenz & S. Battiston & F. Schweitzer, 2009. "Systemic risk in a unifying framework for cascading processes on networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 71(4), pages 441-460, October.
    3. Battiston, Stefano & Delli Gatti, Domenico & Gallegati, Mauro & Greenwald, Bruce & Stiglitz, Joseph E., 2012. "Liaisons dangereuses: Increasing connectivity, risk sharing, and systemic risk," Journal of Economic Dynamics and Control, Elsevier, vol. 36(8), pages 1121-1141.
    4. Joseph E. Stiglitz, 2010. "Risk and Global Economic Architecture: Why Full Financial Integration May Be Undesirable," American Economic Review, American Economic Association, vol. 100(2), pages 388-392, May.
    5. Dimitrios Bisias & Mark Flood & Andrew W. Lo & Stavros Valavanis, 2012. "A Survey of Systemic Risk Analytics," Annual Review of Financial Economics, Annual Reviews, vol. 4(1), pages 255-296, October.
    6. Andrew G. Haldane & Robert M. May, 2011. "Systemic risk in banking ecosystems," Nature, Nature, vol. 469(7330), pages 351-355, January.
    7. Nier, Erlend & Yang, Jing & Yorulmazer, Tanju & Alentorn, Amadeo, 2007. "Network models and financial stability," Journal of Economic Dynamics and Control, Elsevier, vol. 31(6), pages 2033-2060, June.
    8. Battiston, Stefano & Gatti, Domenico Delli & Gallegati, Mauro & Greenwald, Bruce & Stiglitz, Joseph E., 2012. "Default cascades: When does risk diversification increase stability?," Journal of Financial Stability, Elsevier, vol. 8(3), pages 138-149.
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    Cited by:

    1. Konstantinos Spiliopoulos, 2014. "Systemic Risk and Default Clustering for Large Financial Systems," Papers 1402.5352, arXiv.org, revised Feb 2015.
    2. Konstantinos Spiliopoulos & Jia Yang, 2018. "Network effects in default clustering for large systems," Papers 1812.07645, arXiv.org, revised Feb 2020.
    3. Oliver Kley & Claudia Kluppelberg & Lukas Reichel, 2014. "Systemic risk through contagion in a core-periphery structured banking network," Papers 1406.6575, arXiv.org.

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