Large deviations for a mean field model of systemic risk

Josselin Garnier, George Papanicolaou, Tzu Wei Yang

Research output: Contribution to journalArticlepeer-review

62 Scopus citations


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 last one 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.

Original languageEnglish (US)
Pages (from-to)151-184
Number of pages34
JournalSIAM Journal on Financial Mathematics
Issue number1
StatePublished - 2013


  • Dynamic phase transitions
  • Large deviations
  • Mean field
  • Systemic risk


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