Deciding Bank Interest Rates -- A Major-Minor Impulse Control Mean-Field Game Perspective

TL;DR

This paper introduces a novel framework for setting bank interest rates using a major-minor mean field game model, incorporating impulsive control and deep learning to analyze strategic interactions among banks.

Contribution

It develops a new mean field game approach with impulsive control for interbank interest rate decisions, solved via a deep Q-network with a Fictitious Play algorithm.

Findings

The proposed algorithm converges to a Nash Equilibrium.

The model captures complex bank interactions in interest rate setting.

Deep Q-network effectively solves the mean field game.

Abstract

Deciding bank interest rates has been a long-standing challenge in finance. It is crucial to ensure that the selected rates balance market share and profitability. However, traditional approaches typically focus on the interest rate changes of individual banks, often neglecting the interactions with other banks in the market. This work proposes a novel framework that models the interest rate problem as a major-minor mean field game within the context of an interbank game. To incorporate the complex interactions between banks, we utilize mean-field theory and employ impulsive control to model the overhead in rate adjustments. Ultimately, we solve this optimal control problem using a new deep Q-network method, which iterates the parameterized action value functions for major and minor players and updates the networks in a Fictitious Play way. Our proposed algorithm converges, offering a solution that enables the analysis of strategies for major and minor players in the market under the Nash Equilibrium.