Dynamic contagion in a banking system with births and defaults

Tomoyuki Ichiba (), Michael Ludkovski () and Andrey Sarantsev ()
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Tomoyuki Ichiba: University of California
Michael Ludkovski: University of California
Andrey Sarantsev: University of Nevada

Annals of Finance, 2019, vol. 15, issue 4, No 2, 489-538

Abstract: Abstract We consider a dynamic model of interconnected banks. New banks can emerge, and existing banks can default, creating a birth-and-death setup. Microscopically, banks evolve as independent geometric Brownian motions. Systemic effects are captured through default contagion: as one bank defaults, reserves of other banks are reduced by a random proportion. After examining the long-term stability of this system, we investigate mean-field limits as the number of banks tends to infinity. Our main results concern the measure-valued scaling limit which is governed by a McKean–Vlasov jump-diffusion. The default impact creates a mean-field drift, while the births and defaults introduce jump terms tied to the current distribution of the process. Individual dynamics in the limit is described by the propagation of chaos phenomenon. In certain cases, we explicitly characterize the limiting average reserves.

Keywords: Default contagion; Mean field limit; Interacting birth-and-death process; McKean–Vlasov jump-diffusion; Propagation of chaos; Lyapunov function; 60J70; 60J75; 60K35; 91B70 (search for similar items in EconPapers)
JEL-codes: C60 E17 G10 O41 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10436-019-00351-2

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