Large deviations for a mean field model of systemic risk
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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- Jan Lorenz & Stefano Battiston & Frank Schweitzer, 2009.
"Systemic Risk in a Unifying Framework for Cascading Processes on Networks,"
0907.5325, arXiv.org, revised Jan 2010.
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- Battiston, Stefano & Delli Gatti, Domenico & Gallegati, Mauro & Greenwald, Bruce & Stiglitz, Joseph E., 2012.
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ETH-RC-11-006, ETH Zurich, Chair of Systems Design.
- 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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Bank of England working papers
346, Bank of England.
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