Low-rank and graphon limits for dynamic threshold distress contagion in heterogeneous financial networks

Pengbin Feng

Papers from arXiv.org

Abstract: We study distress contagion in financial networks with weighted directed exposures. Losses accumulate while counterparties are below a threshold, allowing institutions to recover. A representation with \(K\) exposure factors reduces the \(N\)-institution dynamics exactly to \(K\) feedback coordinates. For bounded Lipschitz losses, Wasserstein stability of the reduced system and aligned \(L^1\) stability of the directed-kernel equation give error bounds separating population sampling from kernel approximation. For the hard threshold, every bounded nonnegative kernel has a greatest cumulative-distress solution, selected by vanishing positive-side regularization. An Osgood condition on the mass near the threshold along one reference path yields uniqueness, stability, deterministic approximation bounds, and convergence under sampled latent labels. Rank-one examples show that this condition is sharp for uniqueness criteria based only on threshold-layer mass. A branchwise condition verifies the required regularity from the initial profile and kernel. Numerical examples examine low-rank reduction, approximation error, and solution selection; an application to disclosed EBA sovereign holdings constructs exposure factors and evaluates sensitivity bounds.

Date: 2026-08, Revised 2026-09
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