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arXiv · 1912.08695

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

Zachary Feinstein·Andreas Sojmark
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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.

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Zachary Feinstein, Andreas Sojmark. 2019-12-18. A Dynamic Default Contagion Model: From Eisenberg-Noe to the Mean Field. https://arxiv.org/abs/1912.08695

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