The effect of heterogeneity on flocking behavior and systemic risk

TL;DR

This paper investigates how heterogeneity among agents influences flocking behavior and systemic risk in large interconnected systems, providing asymptotic formulas for tail loss probabilities and illustrating the impact through case studies.

Contribution

It introduces a novel analysis of heterogeneity effects on systemic risk and flocking in mean-field models, deriving asymptotic tail loss formulas for large agent populations.

Findings

Heterogeneity significantly affects systemic risk and tail loss probabilities.

Flocking behavior persists despite heterogeneity among agents.

Asymptotic formulas accurately characterize tail risks in large systems.

Abstract

The goal of this paper is to study organized flocking behavior and systemic risk in heterogeneous mean-field interacting diffusions. We illustrate in a number of case studies the effect of heterogeneity in the behavior of systemic risk in the system, i.e., the risk that several agents default simultaneously as a result of interconnections. We also investigate the effect of heterogeneity on the "flocking behavior" of different agents, i.e., when agents with different dynamics end up following very similar paths and follow closely the mean behavior of the system. Using Laplace asymptotics, we derive an asymptotic formula for the tail of the loss distribution as the number of agents grows to infinity. This characterizes the tail of the loss distribution and the effect of the heterogeneity of the network on the tail loss probability.