Pareto Optima for a Class of Singular Control Games

Rama Cont (), Xin Guo and Renyuan Xu
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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

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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.

Keywords: singular stochastic control; interbank markets; stochastic differential game; stochastic control; Pareto optimum; Nash equilibrium; Skorokhod problem; LIBOR rate; mathematical finance (search for similar items in EconPapers)
Date: 2020-12-09
New Economics Papers: this item is included in nep-gth
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