Particle systems with singular interaction through hitting times: application in systemic risk modeling

Understand

We propose an interacting particle system to model the evolution of a system of banks with mutual exposures.

• In this model, a bank defaults when its normalized asset value hits a lower threshold, and its default causes instantaneous losses to other banks, possibly triggering a cascade of defaults.
• The strength of this interaction is determined by the level of the so-called non-core exposure.
• We show that, when the size of the system becomes large, the cumulative loss process of a bank resulting from the defaults of other banks exhibits discontinuities.