PARTICLE SYSTEMS WITH SINGULAR INTERACTION THROUGH HITTING TIMES APPLICATION IN SYSTEMIC RISK MODELING

PARTICLE SYSTEMS WITH SINGULAR INTERACTION THROUGH HITTING TIMES : APPLICATION IN SYSTEMIC RISK MODELING

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. T...

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Veröffentlicht in:The Annals of Applied Probability. - Institute of Mathematical Statistics. - 29(2019), 1, Seite 89-129
1. Verfasser: Nadtochiy, Sergey (VerfasserIn)
Weitere Verfasser: Shkolnikov, Mykhaylo
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 2019
Zugriff auf das übergeordnete Werk:The Annals of Applied Probability
Schlagworte:Banking systems blow-ups in parabolic partial differential equations default cascades interacting particle systems large system limits loss of continuity mean-field models noncore exposures nonlinear Cauchy–Dirichlet problems regularity estimates mehr... self-excitation singular interaction systemic crises systemic risk
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520 |a 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 noncore 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 noncore 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 [Ann. Appl. Probab. 25 (2015) 2096–2133] and [Stochastic Process. Appl. 125 (2015) 2451–2492], 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. 
540 |a © Institute of Mathematical Statistics, 2019 
650 4 |a Banking systems 
650 4 |a blow-ups in parabolic partial differential equations 
650 4 |a default cascades 
650 4 |a interacting particle systems 
650 4 |a large system limits 
650 4 |a loss of continuity 
650 4 |a mean-field models 
650 4 |a noncore exposures 
650 4 |a nonlinear Cauchy–Dirichlet problems 
650 4 |a regularity estimates 
650 4 |a self-excitation 
650 4 |a singular interaction 
650 4 |a systemic crises 
650 4 |a systemic risk 
655 4 |a research-article 
700 1 |a Shkolnikov, Mykhaylo  |e verfasserin  |4 aut 
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