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

arXiv: https://arxiv.org/abs/2005.05766 · HTML: https://mlsanity.com/paper/2005.05766/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 May 2020.

## Built on by (most cited first, 1 of 1)

- [Deviations from the Nash equilibrium in a two-player optimal execution game with reinforcement learning](https://mlsanity.com/paper/2408.11773/) (2024)

## Abstract (arXiv)

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.