Interbank lending with benchmark rates: Pareto optima for a class of singular control games. (13th July 2021)

• Record Type: Journal Article
• Authors: Cont, Rama; Guo, Xin; Xu, Renyuan
• Other Names: Obloj Jan guestEditor.; Zariphopoulou Thaleia guestEditor.
• Is Part Of: Mathematical finance. Volume 31:Number 4(2021)
• Page Start: 1357
• Page End: 1393
• Publication Date: 2021-07-13
• Subjects: interbank markets -- LIBOR rate -- Nash equilibrium -- Pareto optimum -- singular stochastic control -- Skorokhod problem -- stochastic differential game; Business mathematics -- Periodicals; 332
• DOI: 10.1111/mafi.12325
• Languages: English
• ISSNs: 0960-1627

Abstract

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.