Optimal bailout strategies resulting from the drift controlled supercooled Stefan problem

• Main Authors: Cuchiero, Christa, Reisinger, Christoph, Rigger, Stefan
• Format: Journal Article
• Language: English
• Published: 02.11.2021
• Subjects: Mathematics - Optimization and Control; Mathematics - Probability; Quantitative Finance - Mathematical Finance
• DOI: 10.48550/arxiv.2111.01783

We consider the problem faced by a central bank which bails out distressed financial institutions that pose systemic risk to the banking sector. In a structural default model with mutual obligations, the central agent seeks to inject a minimum amount of cash in order to limit defaults to a given proportion of entities. We prove that the value of the central agent's control problem converges as the number of defaultable institutions goes to infinity, and that it satisfies a drift controlled version of the supercooled Stefan problem. We compute optimal strategies in feedback form by solving numerically a regularized version of the corresponding mean field control problem using a policy gradient method. Our simulations show that the central agent's optimal strategy is to subsidise banks whose equity values lie in a non-trivial time-dependent region.