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Optimal bailout strategies resulting from the drift controlled supercooled Stefan problem

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  • Christa Cuchiero
  • Christoph Reisinger
  • Stefan Rigger

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.

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  • Christa Cuchiero & Christoph Reisinger & Stefan Rigger, 2021. "Optimal bailout strategies resulting from the drift controlled supercooled Stefan problem," Papers 2111.01783, arXiv.org, revised Oct 2022.
    • Handle: RePEc:arx:papers:2111.01783
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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. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
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