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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
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    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.

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    File URL: http://arxiv.org/pdf/1204.3536
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1204.3536.

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    Date of creation: Apr 2012
    Date of revision: Aug 2012
    Handle: RePEc:arx:papers:1204.3536

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    Web page: http://arxiv.org/

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    1. 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, vol. 71(4), pages 441-460, October.
    2. Stefano Battiston & Domenico Delli Gatti & Mauro Gallegati & Bruce Greenwald & Joseph E. Stiglitz, . "Default Cascades: When Does Risk Diversification Increase Stability?," Working Papers ETH-RC-11-006, ETH Zurich, Chair of Systems Design.
    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. 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.
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    Cited by:
    1. Konstantinos Spiliopoulos, 2014. "Systemic Risk and Default Clustering for Large Financial Systems," Papers 1402.5352, arXiv.org.
    2. Oliver Kley & Claudia Kl\"uppelberg & Lukas Reichel, 2014. "Systemic risk through contagion in a core-periphery structured banking network," Papers 1406.6575, arXiv.org.

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