TL;DR
This paper models systemic risk in banking via coupled Feller diffusions, analyzing how liquidity and deposit rates influence bank defaults and system stability through a mean field game framework.
Contribution
It introduces a novel coupled diffusion model for banking systems and explores equilibrium strategies affecting liquidity, deposit rates, and default risks.
Findings
Adding liquidity causes a flocking effect among banks.
Higher deposit rates reduce the growth of total reserves.
The model predicts increased defaults under certain conditions.
Abstract
We propose a simple model of the banking system incorporating a game feature where the evolution of monetary reserve is modeled as a system of coupled Feller diffusions. The Markov Nash equilibrium generated through minimizing the linear quadratic cost subject to Cox-Ingersoll-Ross type processes creates liquidity and deposit rate. The adding liquidity leads to a flocking effect but the deposit rate diminishes the growth rate of the total monetary reserve causing a large number of bank defaults. In addition, the corresponding Mean Field Game and the infinite time horizon stochastic game with the discount factor are also discussed.
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Taxonomy
TopicsStochastic processes and financial applications · Economic theories and models · Complex Systems and Time Series Analysis