• Corpus ID: 240419862

Optimal bailout strategies resulting from the drift controlled supercooled Stefan problem

@inproceedings{Cuchiero2021OptimalBS,
  title={Optimal bailout strategies resulting from the drift controlled supercooled Stefan problem},
  author={Christa Cuchiero and Christoph Reisinger and Stefan Rigger},
  year={2021}
}

• Christa Cuchiero, C. Reisinger, Stefan Rigger
• Published 2 November 2021
• Mathematics

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 forward-backward coupled system of PDEs. Our simulations show that the central agent’s optimal strategy is to subsidise banks whose asset values lie in a non-trivial time-dependent region. Finally, we study a linear-quadratic version of the model where instead of the terminal losses, the agent optimises a terminal cost function of the equity values. In this case, we are able to give semi-analytic strategies, which we again illustrate numerically.