Particle systems with singular interaction through hitting times: Application in systemic risk modeling
By Sergey Nadtochiy, Mykhaylo Shkolnikov. The Annals of Applied Probability, 2017
76 citations recorded by the source corpus.
We propose an interacting particle system to model the evolution of a system of banks with mutual exposures. In this model, a bank defaults when its normalized asset value hits a lower threshold, and its default causes instantaneous losses to other banks, possibly triggering a cascade of defaults. The strength of this interaction is determined by the level of the so-called non-core exposure. We show that, when the size of the system becomes large, the cumulative loss process of a bank resulting from the defaults of other banks exhibits discontinuities. These discontinuities are naturally interpreted as systemic events, and we characterize them explicitly in terms of the level of non-core exposure and the fraction of banks that are "about to default". The main mathematical challenges of our work stem from the very singular nature of the interaction between the particles, which is inherited by the limiting system. A similar particle system is analyzed in [DIRT15a] and [DIRT15b], and we build on and extend their results. In particular, we characterize the large-population limit of the system and analyze the jump times, the regularity between jumps, and the local uniqueness of the limiting process.
Subfields: Finance, Mathematical Physics, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/2f7342c8fbb6d5b5cad912ac1f6edce6f4804f5d
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Finance
In Mathematical Physics
In Public Health, Environmental and Occupational Health
Citations in the corpus
- A McKean–Vlasov equation with positive feedback and blow-ups (2018, methodology): “With regard to the financial framework introduced above, we note that a similar model for default contagion (with constant drift and volatility) was recently proposed in [14].”