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

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.