Mean field game of mutual holding with defaultable agents, and systemic risk
Probability
2023-03-15 v1 Risk Management
Abstract
We introduce the possibility of default in the mean field game of mutual holding of Djete and Touzi [11]. This is modeled by introducing absorption at the origin of the equity process. We provide an explicit solution of this mean field game. Moreover, we provide a particle system approximation, and we derive an autonomous equation for the time evolution of the default probability, or equivalently the law of the hitting time of the origin by the equity process. The systemic risk is thus described by the evolution of the default probability.
Cite
@article{arxiv.2303.07996,
title = {Mean field game of mutual holding with defaultable agents, and systemic risk},
author = {Mao Fabrice Djete and Gaoyue Guo and Nizar Touzi},
journal= {arXiv preprint arXiv:2303.07996},
year = {2023}
}