  We propose a dynamic mean field model for `systemic risk' in large financial
systems, which we derive from a system of interacting diffusions on the
positive half-line with an absorbing boundary at the origin. These diffusions
represent the distances-to-default of financial institutions and absorption at
zero corresponds to default. 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 this way, we aim to capture
key `system-wide' effects on risk. The resulting mean field limit is
characterized uniquely by a nonlinear SPDE on the half-line with a Dirichlet
boundary condition. The density of this SPDE gives the conditional law of a
non-standard `conditional' McKean--Vlasov diffusion, for which we provide a
novel upper Dirichlet heat kernel type estimate that is essential to the
proofs. Depending on the realizations of the common noise and the rate of mean
reversion, the SPDE can exhibit rapid accelerations in the loss of mass at the
boundary. In other words, the contagion mechanism can give rise to periods of
significant systemic default clustering.
