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Optimal bailout strategies resulting from the drift controlled supercooled Stefan problem

Author

Listed:
  • Christa Cuchiero

    (Vienna University)

  • Christoph Reisinger

    (University of Oxford)

  • Stefan Rigger

    (Vienna University)

Abstract

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.

Suggested Citation

  • Christa Cuchiero & Christoph Reisinger & Stefan Rigger, 2024. "Optimal bailout strategies resulting from the drift controlled supercooled Stefan problem," Annals of Operations Research, Springer, vol. 336(1), pages 1315-1349, May.
    • Handle: RePEc:spr:annopr:v:336:y:2024:i:1:d:10.1007_s10479-023-05293-7
    DOI: 10.1007/s10479-023-05293-7
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    References listed on IDEAS

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    3. Andrey Itkin & Alexander Lipton, 2017. "Structural default model with mutual obligations," Review of Derivatives Research, Springer, vol. 20(1), pages 15-46, April.
    4. Delarue, F. & Inglis, J. & Rubenthaler, S. & Tanré, E., 2015. "Particle systems with a singular mean-field self-excitation. Application to neuronal networks," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2451-2492.
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