Interacting Particle Systems for Systemic Risk

Systemic Risk: Motivation Stochastic Model Simulating Systemic Shocks Examples of Rare EventsToy ExampleX t = W t − cN t jump-diffusion model (c ≫ 1)Rare event is : A = {X T ∈ −da}G(x t , x t−1 ) = exp(−α(x t − x t−1 )) gives a strong preference toparticles that jump.G(x t , x t−1 ) = exp(−α(x t − x t−1 ))∧M is more "democratic" andcreates a more diverse ancestral tree with minimal efficiency loss0G = exp(−0.4(x p−x p−1))−10−20−300 5 10 15 20100−10−20−30G = exp(−0.4 max(x p−x p−1,18))−400 5 10 15 20Figure: Ancestral Trees for 2 different FK potentials.23LudkovskiSystemic Risk