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Pareto Optima for a Class of Singular Control Games

Author

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  • Rama Cont

    (LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation - UPD7 - Université Paris Diderot - Paris 7 - SU - Sorbonne Université - CNRS - Centre National de la Recherche Scientifique, MI - Mathematical Institute [Oxford] - University of Oxford)

  • Xin Guo

    (UC Berkeley - University of California [Berkeley] - UC - University of California)

  • Renyuan Xu

    (MI - Mathematical Institute [Oxford] - University of Oxford)

Abstract

We study a class of N-player stochastic differential games of singular control, motivated by the study of a dynamic model of interbank lending with benchmark rates. We describe Pareto optima for this game and show how they may be achieved through the intervention of a regulator, whose policy is a solution to a singular stochastic control problem. Pareto optima are characterized in terms of the solution to a new class of Skorokhod problems with piecewise-continuous free boundary. Pareto optimal policies are shown to correspond to the enforcement of endogenous bounds on interbank lending rates. Analytical comparison between Pareto optima and Nash equilibria for the case of two players allows to quantify the impact of regulatory intervention on the stability of the interbank rate.

Suggested Citation

  • Rama Cont & Xin Guo & Renyuan Xu, 2020. "Pareto Optima for a Class of Singular Control Games," Working Papers hal-03049246, HAL.
    • Handle: RePEc:hal:wpaper:hal-03049246
    Note: View the original document on HAL open archive server: https://hal.science/hal-03049246v1
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    References listed on IDEAS

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    Cited by:

    1. Almendra Awerkin & Tiziano Vargiolu, 2021. "Optimal installation of renewable electricity sources: the case of Italy," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 1179-1209, December.
    2. Dianetti, Jodi & Ferrari, Giorgio, 2021. "Multidimensional Singular Control and Related Skorokhod Problem: Suficient Conditions for the Characterization of Optimal Controls," Center for Mathematical Economics Working Papers 645, Center for Mathematical Economics, Bielefeld University.

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