A Dynamic Default Contagion Model: From Eisenberg-Noe to the Mean Field

TL;DR

This paper introduces a new model for financial default contagion that merges Eisenberg-Noe networks with dynamic mean field interactions, enabling analysis of systemic risk in large interconnected financial systems.

Contribution

It bridges the Eisenberg-Noe network approach with mean field models, providing a new framework for analyzing systemic risk in large financial networks.

Findings

Mean field interaction is the limit of finite Eisenberg-Noe networks.

The mean field model is well-posed and respects network topology.

Provides a new analytical tool for systemic risk modeling.

Abstract

In this work we introduce a model of default contagion that combines the approaches of Eisenberg-Noe interbank networks and dynamic mean field interactions. The proposed contagion mechanism provides an endogenous rule for early defaults in a network of financial institutions. The main result is to demonstrate a mean field interaction that can be found as the limit of the finite bank system generated from a finite Eisenberg-Noe style network. In this way, we connect two previously disparate frameworks for systemic risk, and in turn we provide a bridge for exploiting recent advances in mean field analysis when modelling systemic risk. The mean field limit is shown to be well-posed and is identified as a certain conditional McKean-Vlasov type problem that respects the original network topology under suitable assumptions.