Interacting Particle Systems for Systemic Risk

More documents

Recommendations

Info

Systemic Risk: Motivation Stochastic Model Simulating Systemic Shocks Examples of Rare EventsIS ApproximationApproximate:E[f(X(T))] = E[f(X(T))= η T (˜f(X))T∏k=1G −1kT∏η k (G k ),k=1η k (g) = γ k (g)/γ k (1)(X)]T∏G k (X)k=1γ k (g) := E [ g(X)˜f(X) := f(X(T)) T ∏k=1k∏G l (X) ] .l=1G −1k(X)Obtain an unbiased estimator based onη (J)k(G k ) = 1 ∑ JJ j=1 G k(X (j) ).Typical ( potential: G k (X (j) (t 0 ), X (j) (t 1 ),... ) X (j) (t k )) =exp α(min l≤k−1 N(t l )−min l≤k N(t l )) (multiplicative).Preference to particles where N(t) is setting new lows.15LudkovskiSystemic Risk
Systemic Risk: Motivation Stochastic Model Simulating Systemic Shocks Examples of Rare EventsImportance Sampling140120Original MeasureEmpirical IS for low mint N(t)10080604020040 50 60 70 80 90 100 110mint N(t)Figure: Histogram of 400 MC simulations: under original measure (independent scenarios) andusing a F-K potential G k (X) = exp(−α(min l≤k N(l)−min l
Page 1: Systemic Risk: Motivation Stochasti
Page 4 and 5: Systemic Risk: Motivation Stochasti

Interacting Particle Systems for Systemic Risk

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?