# Large Banking Systems with Default and Recovery: A Mean Field Game Model

@article{Elie2020LargeBS, title={Large Banking Systems with Default and Recovery: A Mean Field Game Model}, author={Romuald Elie and Tomoyuki Ichiba and Mathieu Lauri{\`e}re}, journal={arXiv: Optimization and Control}, year={2020} }

We consider a mean-field model for large banking systems, which takes into account default and recovery of the institutions. Building on models used for groups of interacting neurons, we first study a McKean-Vlasov dynamics and its evolutionary Fokker-Planck equation in which the mean-field interactions occur through a mean-reverting term and through a hitting time corresponding to a default level. The latter feature reflects the impact of a financial institution's default on the global…

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## References

SHOWING 1-10 OF 26 REFERENCES

### An SPDE model for systemic risk with endogenous contagion

- MathematicsFinance and Stochastics
- 2019

We propose a dynamic mean-field model for ‘systemic risk’ in large financial systems, derived from a system of interacting diffusions on the positive half-line with an absorbing boundary at the…

### Mean Field Games and Systemic Risk

- Economics
- 2013

We propose a simple model of inter-bank borrowing and lending where the evolution of the log-monetary reserves of $N$ banks is described by a system of diffusion processes coupled through their…

### Particle systems with singular interaction through hitting times: Application in systemic risk modeling

- EconomicsThe Annals of Applied Probability
- 2019

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…

### Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle

- MathematicsCommun. Inf. Syst.
- 2006

The McKean-Vlasov NCE method presented in this paper has a close connection with the statistical physics of large particle systems: both identify a consistency relationship between the individual agent at the microscopic level and the mass of individuals at the macroscopic level.

### A McKean–Vlasov equation with positive feedback and blow-ups

- MathematicsThe Annals of Applied Probability
- 2019

We study a McKean--Vlasov equation arising from a mean-field model of a particle system with positive feedback. As particles hit a barrier they cause the other particles to jump in the direction of…

### At the mercy of the common noise: blow-ups in a conditional McKean–Vlasov Problem

- Mathematics
- 2018

We extend a model of positive feedback and contagion in large mean-field systems by introducing a common source of noise driven by Brownian motion. Although the dynamics in the model are continuous,…

### Mean field games

- Mathematics
- 2007

Abstract.We survey here some recent studies concerning what we call mean-field models by analogy with Statistical Mechanics and Physics. More precisely, we present three examples of our mean-field…

### Mean field systems on networks, with singular interaction through hitting times

- MathematicsThe Annals of Probability
- 2020

Building on the line of work [DIRT15a], [DIRT15b], [NS17a], [DT17], [HLS18], [HS18] we continue the study of particle systems with singular interaction through hitting times. In contrast to the…

### Mean Field Games: Numerical Methods

- Computer ScienceSIAM J. Numer. Anal.
- 2010

Numerical methods for the approximation of the stationary and evolutive versions of stochastic differential game models are proposed here and existence and uniqueness properties as well as bounds for the solutions of the discrete schemes are investigated.

### Individual and mass behaviour in large population stochastic wireless power control problems: centralized and Nash equilibrium solutions

- Mathematics42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475)
- 2003

We consider uplink power control for lognormal fading channels in the large population case. First, we examine the structure of the control law in a centralized stochastic optimal control setup. We…