Large deviations for a mean field model of systemic risk

TL;DR

This paper analyzes a mean field model of systemic risk using large deviations theory, showing how cooperation among agents affects individual stability and systemic risk in a stochastic interacting system.

Contribution

It provides a detailed large deviations analysis of a mean field diffusion model with bistable potential, revealing the dual effect of cooperation on stability and systemic risk.

Findings

Increasing cooperation can enhance individual stability.

Higher cooperation levels may elevate systemic risk.

The model quantifies the trade-off between stability and systemic risk.

Abstract

We consider a system of diffusion processes that interact through their empirical mean and have a stabilizing force acting on each of them, corresponding to a bistable potential. There are three parameters that characterize the system: the strength of the intrinsic stabilization, the strength of the external random perturbations, and the degree of cooperation or interaction between them. The latter is the rate of mean reversion of each component to the empirical mean of the system. We interpret this model in the context of systemic risk and analyze in detail the effect of cooperation between the components, that is, the rate of mean reversion. We show that in a certain regime of parameters increasing cooperation tends to increase the stability of the individual agents but it also increases the overall or systemic risk. We use the theory of large deviations of diffusions interacting through their mean field.