Interacting Particle Systems for Systemic Risk

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Systemic Risk: Motivation Stochastic Model Simulating Systemic Shocks Examples of Rare EventsNumerical ChallengesFor estimating rare event probabilities we have a well-developedtheory based on large deviationsThe method provides an estimate of the CoV that can be used toguide potential function selection and evaluation of theperformance.In practice, these estimates are quite stable.We are also interested in the conditional trajectories to rareevents. Here it is hard to check accuracy/efficiency. Numericalevidence suggests that different potentials are more efficient forthis task.Shape of the potential strongly affects the shape of the ancestraltree (reward the fit vs. cull the weak)Splitting Methods vs. Exponential Tilting.21LudkovskiSystemic Risk
Systemic Risk: Motivation Stochastic Model Simulating Systemic Shocks Examples of Rare EventsWork in ProgressHave a framework for simulating dynamic defaults in an interactingnetwork.Understanding the relationships and mechanisms of rare eventsunlocks many interesting phenomena (a cascade of small defaultsvs. a single large event).Another analytic tool is the LLN scaling limit as N(0) → ∞(average out the noise from the defaults and births).THANK YOU!22LudkovskiSystemic Risk
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Interacting Particle Systems for Systemic Risk

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