Particle systems and systemic risk

Systemic risk in the banking system is the risk that small losses and defaults can escalate through endogenous effects to cause an event affecting large parts of the financial sector. We will consider some simple particle system models for the interactions between banks and show how this leads to stochastic McKean-Vlasov equations describing the whole system. The systemic risk can be captured through a loss function and we will show that this can have unexpected behaviour in different models.