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

arXiv: https://arxiv.org/abs/2001.10206 · HTML: https://mlsanity.com/paper/2001.10206/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jan 2020.

## Built on by (most cited first, 2 of 2)

- [Deep Learning for Mean Field Games and Mean Field Control with Applications to Finance](https://mlsanity.com/paper/2107.04568/) (2021)
- [Learning Sparse Graphon Mean Field Games](https://mlsanity.com/paper/2209.03880/) (2022)

## Abstract (arXiv)

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 distribution of reserves in the banking system. The systemic risk problem of financial institutions is understood as a blow-up phenomenon of the Fokker-Planck equation. Then, we incorporate in the model an optimization component by letting the institutions control part of their dynamics in order to minimize their expected risk. Phrasing this optimization problem as a mean-field game, we provide an explicit solution in a special case and, in the general case, we report numerical experiments based on a finite difference scheme.