MEAN FIELD GAME OF MUTUAL HOLDING WITH DEFAULTABLE AGENTS, AND SYSTEMIC RISK

We introduce the possibility of default in the mean field game of mutual holding of Djete and Touzi [14]. This is modeled by introducing absorption at the origin of the equity process. We provide an explicit solution of this mean field game together with a particle system approximation. The systemic risk is described by the evolution of the default probability which characterizes the law of the hitting time of the origin by the equity process. We provide an equation for the time evolution of the default probability which is autonomous in the sense that it does not involve the distribution of the equity process.