Limiting Contagion Risk in the Banking System: An Indirect Optimal Control Approach for Financial Stablity

Abstract We aim to explore the application of compartmental models originally developed in epi-demiology to the analysis of economic and financial dynamics, such as banking contagionand market panics. These models divide a system into subpopulations (for example, solventor defaulting agents) to represent systemic instability in an aggregate and structured way.This work proposes integrating these models with optimal control theory, a mathematicalapproach that enables regulators or private actors to design e¤ective intervention strategiessuch as liquidity injections or interest rate adjustments to contain the spread of financial riskwhile minimizing costs and adhering to dynamic constraints. The objective is to developa unified framework that combines compartmental modeling and optimal control, specifically tailored to financial contagion. The goal is to quantify the trade-offs between financialstability and the cost of interventions.