Mean field game of mutual holding with defaultable agents, and systemic risk

TL;DR

This paper extends the mean field game of mutual holding to include default risk by modeling absorption at zero, providing explicit solutions, particle system approximations, and an autonomous default probability evolution equation to analyze systemic risk.

Contribution

It introduces default modeling into the mean field game framework, deriving explicit solutions and a new autonomous equation for default probability evolution.

Findings

Explicit solution for the default-inclusive mean field game

Particle system approximation for the model

Autonomous equation for default probability evolution

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.