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Interbank lending with benchmark rates: Pareto optima for a class of singular control games

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  • Rama Cont
  • Xin Guo
  • Renyuan Xu

Abstract

We analyze a class of 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 solutions 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 provides insight into the impact of regulatory intervention on the stability of interbank rates.

Suggested Citation

  • Rama Cont & Xin Guo & Renyuan Xu, 2021. "Interbank lending with benchmark rates: Pareto optima for a class of singular control games," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1357-1393, October.
    • Handle: RePEc:bla:mathfi:v:31:y:2021:i:4:p:1357-1393
    DOI: 10.1111/mafi.12325
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    References listed on IDEAS

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    Cited by:

    1. Dianetti, Jodi & Ferrari, Giorgio, 2023. "Multidimensional singular control and related Skorokhod problem: Sufficient conditions for the characterization of optimal controls," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 547-592.
    2. Dianetti, Jodi, 2023. "Linear-Quadratic-Singular Stochastic Differential Games and Applications," Center for Mathematical Economics Working Papers 678, Center for Mathematical Economics, Bielefeld University.

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