This paper proposes a continuous-time dynamic clearing model on a multilayer financial network to study systemic risk propagation and optimal intervention. The model incorporates interbank credit, equity crossholdings, and overlapping portfolios, and models bankruptcy as a jump event triggered by insolvency or illiquidity. Based on the system’s dynamic structure, we develop a model predictive control (MPC) framework that enables forward-looking and flexible allocation of limited bailout resources between debt relief and capital injection. Numerical results show that the proposed MPC strategy substantially outperforms both no-intervention and rule-based policies in terms of financial stability and resource efficiency. Compared with no intervention, the MPC strategy reduces the number of defaulting banks by approximately 56%. In contrast, the simple rule-based intervention achieves a reduction of about 48.83%, while improving rescue efficiency by approximately 28.57%. Overall, the framework provides a unified and effective approach to systemic risk control in financial networks.
Ding et al. (2026) studied this question.