We propose a dynamic model for the stability of a large financial network , which we formulate as a system of interacting diffusions on the positive half-line with an absorbing boundary at zero. These diffusions represent the distances-to-default of the financial institutions in the network . As a way of modelling correlated exposures and herd behaviour, we consider a common source of noise and a form of mean-reversion in the drift. Moreover, we introduce an endogenous contagion mechanism whereby the default of one institution can lead to a drop in the distances-to-default of the other institutions. In order to have a general model for systemic (or macroscopic) events, we show that the above system converges to a unique mean field limit , which is characterized by a nonlinear SPDE on the half-line  with a Dirichlet boundary condition  . Depending on the realisations of the common noise and the strength of the mean reversion, this SPDE can exhibit rapid accelerations in the loss of mass at the boundary. In other words,  there are events of small probability that  can give rise to systemic default cascades sparked by a devaluation of the common exposures and amplified by herd behaviour .
We propose a dynamic model for systemic risk in a large financial system , which we formulate as a system of interacting diffusions on the positive half-line with an absorbing boundary at zero. These diffusions represent the distances-to-default of the financial institutions . As a way of modelling correlated exposures and herd behaviour, we consider a common source of noise and a form of mean-reversion in the drift. Moreover, we introduce an endogenous contagion mechanism whereby the default of one institution can cause a drop in the distances-to-default of the other institutions. In order to have a general model for systemic (or macroscopic) events, we show that the system converges to a unique mean field limit characterized by a nonlinear SPDE on the half-line ( with a Dirichlet boundary condition ) which governs the conditional law of a 'conditional McKean-Vlasov' type diffusion . Depending on the realizations of the common noise and the strength of the mean reversion, the SPDE can exhibit rapid accelerations in the loss of mass at the boundary. In other words, sparked by a devaluation of the common exposures, there are events of small probability that , through amplification by herd behaviour, can give rise to systemic default cascades .
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