Coordinated Mean-Field Control for Systemic Risk

TL;DR

This paper introduces a robust mean-field control framework for systemic risk, optimizing central bank policies under adversarial uncertainty with explicit solutions and revealing critical dynamics like loss-of-control regimes.

Contribution

It develops a novel linear-quadratic mean-field control model incorporating multiple policy instruments and interactive dynamics, providing explicit feedback controls and analytical insights.

Findings

Identification of loss-of-control regimes due to robustness breakdown

Demonstration of asymmetry in mean and variance sensitivity

Highlighting the importance of instrument complementarity in systemic risk

Abstract

We develop a robust linear-quadratic mean-field control framework for systemic risk under model uncertainty, in which a central bank jointly optimizes interest rate policy and supervisory monitoring intensity against adversarial distortions. Our model features multiple policy instruments with interactive dynamics, implemented via a variance weight that depends on the policy rate, generating coupling effects absent in single-instrument models. We establish viscosity solutions for the associated HJB--Isaacs equation, prove uniqueness via comparison principles, and provide verification theorems. The linear-quadratic structure yields explicit feedback controls derived from a coupled Riccati system, preserving analytical tractability despite adversarial uncertainty. Simulations reveal distinct loss-of-control regimes driven by robustness-breakdown and control saturation, alongside a pronounced asymmetry in sensitivity between the mean and variance channels. These findings demonstrate the importance of instrument complementarity in systemic risk modeling and control.