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

Paper: arXiv 2303.07996

Authors: Mao Fabrice Djete, Gaoyue Guo, Nizar Touzi

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.

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a sophisticated mathematical extension of mean field games to model mutual holding with defaultable agents and systemic risk, deriving explicit solutions and particle system approximations. However, it is purely theoretical and completely lacks empirical backtesting or real-world financial data validation.

Research Flowchart

  flowchart TD
    A[Research Goal: Model Systemic Risk & Default in MFG of Mutual Holding] --> B[Model Formulation: Equity Dynamics with Absorption at Boundary]
    B --> C[Particle System Approximation & Mean Field Limit]
    C --> D[Explicit Solution of Mean Field Game]
    C --> E[Derive Autonomous Equation for Default Probability Evolution]
    D & E --> F[Outcomes: Characterization of Systemic Risk & Hitting Time Distribution]