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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.
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This content will become publicly available on February 5, 2026
Systemic Robustness: A Mean‐Field Particle System Approach
ABSTRACT This paper is concerned with the problem of capital provision in a large particle system modeled by stochastic differential equations involving hitting times, which arises from considerations of systemic risk in a financial network. Motivated by Tang and Tsai, we focus on the number or proportion of surviving entities that never default to measure the systemic robustness. First we show that the mean‐field particle system and its limit McKean–Vlasov equation are both well‐posed by virtue of the notion of minimal solutions. We then establish a connection between the proportion of surviving entities in the large particle system and the probability of default in the McKean–Vlasov equation as the size of the interacting particle system tends to infinity. Finally, we study the asymptotic efficiency of capital provision for different drift , which is linked to the economy regime: The expected number of surviving entities has a uniform upper bound if ; it is of order if ; and it is of order if , where the effect of capital provision is negligible.
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- Award ID(s):
- 2206038
- PAR ID:
- 10612823
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Mathematical Finance
- ISSN:
- 0960-1627
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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