Mean-Field Models for Systemic Risk with Common Exposures and Contagion

In this talk I will present a mean-field model of `systemic risk' in large financial markets, seeking to capture simple notions of herding, common exposures, and default contagion. The mean-field limit (modelling the macroscopic health of the financial system) is described by a nonlinear SPDE on the positive half-line, which is the stochastic Fokker–Planck equation for an absorbing (conditional) McKean–Vlasov type SDE with common noise. During the talk, I will present results on the well-posedness along with some numerical illustrations. Moreover, I will consider a more singular variant of the mean-field limit, which can exhibit jump discontinuities coming from macroscopic cascades of contagion. In this latter case, I will present some results on how the occurrence of these discontinuities depend on the common noise. The talk is based on joint works with Ben Hambly and Sean Ledger.

Event Topic

Mathematical Finance, Stochastic Analysis, and Machine Learning