Noise induced Stability of a Mean-Field model of Systemic Risk with uncertain robustness

TL;DR

This paper investigates how uncertainty and different interpretations of noise influence the stability of a systemic risk model, revealing phenomena like noise-induced stability that are absent in deterministic settings.

Contribution

It introduces a novel analysis of a McKean-Vlasov SDE with uncertain potential and independent noise types, uncovering complex phase behaviors and noise-induced stability effects.

Findings

Noise can induce stability in the system.

Phase transitions depend on stochastic integral interpretation.

Uncertainty in the potential leads to richer dynamics.

Abstract

We consider a model for systemic risk comprising of a system of diffusion processes, interacting through their empirical mean. Each process is subject to a confining double-well potential with some uncertainty in the coefficients, corresponding to fluctuations in height of the potential barrier seperating the two wells. This is equivalent to studying a single McKean-Vlasov SDE with explicit dependence on its moments and, novelly, independently varying additive and multiplicative noise. Such non-linear SDEs are known to possess two phases: stable (ordered) and unstable (disordered). When the potential is purely bistable, the phase changes from stable to unstable when noise intensity is increased past a critical threshold. With the recent advances, it will be shown that the behaviour here is far richer: indeed, depending on the interpretation of the stochastic integral, the system exhibits phase changes that cannot occur in any regime where there is no uncertainty in the potential. Strikingly, this allows for the phenomenon of noise induced stability; situations where more noise can reduce the risk of system failure.