Financial Mathematics Seminar: "A mean-field model for contagion in large financial systems"

Abstract: In this talk, we will consider a toy model for a large financial system, where each financial entity is identified with a stochastic process modelling its distance-to-default (or some notion of liquidity). Whenever there is a default, the defaulted entity is removed from the system and this then has a contagious effect that causes a drop in the other distances-to-default. As this may in turn force further entities into distress, a positive feedback loop is created, which can act as a simplified model for spirals of financial contagion. Assuming sufficient symmetry, we can show convergence of this system to a unique McKean–Vlasov problem, which allows for a macroscopic analysis of contagion and opens the door for simpler numerical simulation. During the talk, we will outline some surprising qualitative properties of this mean-field limit and discuss recent results on its well-posedness. The talk is based on joint work with Ben Hambly and Sean Ledger.

Host: Jose Figueroa-Lopez