Interacting Particle Systems for Systemic Risk

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Systemic Risk: Motivation Stochastic Model Simulating Systemic Shocks Examples of Rare EventsIndividual dynamics:∫ tX i (t) = X i (g i )+g i∞∑r i X i (s)ds− θ(X j (d j −), X(d j −))X i (d j −)1 {gi
Systemic Risk: Motivation Stochastic Model Simulating Systemic Shocks Examples of Rare EventsSample Path of System Dynamics1.210.80.60.40.200 5 10 15 20 25 30 35 40 45 50Time t¯X(t)N(t)/N(0)1Default Size0.80.60.40.200 5 10 15 20 25 30 35 40 45 50170 Total DefaultsFigure: Trajectory of mean asset size X(t) and normalized number of banks N(t)/N(0).Bottom panel: default times and corresponding impact proportions θ(·). We take r = 0.02,λ − (x) = 0.05/(1+x), λ + (n) = 300/(1+n), ξ ∼ Exp(1) and N 0 = 100 andθ(x j ,¯x) ∼ Beta( x j100¯x , 1). Ludkovski Systemic Risk8
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Interacting Particle Systems for Systemic Risk

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