2017/05/01 by Sergey Nadtochiy, Nadtochiy, Sergey, Mykhaylo Shkolnikov +1 · 2 citations
Mathematics · Medicine · Physics and Astronomy · #35K10 #35K60 #60H30 #82C22 #91G80 #Analysis of PDEs (math.AP) #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1705.00691
openalex publication_date 2017/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose an interacting particle system to model the evolution of a system\nof banks with mutual exposures. In this model, a bank defaults when its\nnormalized asset value hits a lower threshold, and its default causes\ninstantaneous losses to other banks, possibly triggering a cascade of defaults.\nThe strength of this interaction is determined by the level of the so-called\nnon-core exposure. We show that, when the size of the system becomes large, the\ncumulative loss process of a bank resulting from the defaults of other banks\nexhibits discontinuities. These discontinuities are naturally interpreted as\nsystemic events, and we characterize them explicitly in terms of the level of\nnon-core exposure and the fraction of banks that are "about to default". The\nmain mathematical challenges of our work stem from the very singular nature of\nthe interaction between the particles, which is inherited by the limiting\nsystem. A similar particle system is analyzed in [DIRT15a] and [DIRT15b], and\nwe build on and extend their results. In particular, we characterize the\nlarge-population limit of the system and analyze the jump times, the regularity\nbetween jumps, and the local uniqueness of the limiting process.\n