Interacting Particle Systems for Systemic Risk

Systemic Risk: Motivation Stochastic Model Simulating Systemic Shocks Examples of Rare EventsFeynman Kac PotentialsConsider a collection of J scenario path-particles X (j) , j = 1,...,J.The particles evolve according to a Feynman-Kac measurechange:d˜PdP | F T= 1Z TT ∏k=1G k (X)where G k are the Feynman-Kac potentials on the increasing pathspaces of length k: G k (X) ≡ G k (X(t 0 ), X(t 1 ),..., X(t k )).Sequential algorithm: At dates t k re-sample particles usingweights w j := G k(X (j) )∑l G k(X l ) .Propagate particles independently using P-dynamics.14LudkovskiSystemic Risk