# Christa Cuchiero - Optimal bailout strategies resulting from the drift controlled supercooled Stefan problem

Dates: | 30 March 2022 |
---|---|

Times: | 13:30 - 14:30 |

What is it: | Seminar |

Organiser: | Department of Mathematics |

Christa Cuchiero (University of Vienna) will speak in the Probability seminar.

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 to a subset of the entities in order to limit defaults to a given proportion of entities. We prove that the value of the agent's control problem converges as the number of defaultable agents goes to infinity, and that this mean-field limit 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 agent's optimal strategy is to subsidise banks whose asset values lie in a non-trivial time-dependent region. We also study a linear-quadratic version of the model where instead of the terminal losses, the agent optimizes a terminal cost function of the equity values. In this case, we are able to give semi-analytic strategies, which we again illustrate numerically. The talk is based on joint work with Christoph Reisinger and Stefan Rigger.