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

Pengbin Feng

Papers from arXiv.org

Abstract: We study how financial distress propagates through a directed network when institutions can recover and become distressed again. Each institution's current buffer determines its loss transmission rate, so the duration of distress affects its creditors' cumulative losses. We show that the dynamics of a network with $K$ sender--receiver factor pairs can be represented exactly by a closed system of $K$ feedback equations. For bounded Lipschitz loss rates, we prove stability with respect to population and exposure changes, using Wasserstein distance for type distributions and aligned norms for kernels. These estimates quantify the error in approximating a directed graphon model by finite factor networks. Hard thresholds introduce a further difficulty: when many institutions lie close to the threshold, the same initial data can admit several contagion paths. For bounded nonnegative kernels and bounded initial profiles, we construct the greatest cumulative-distress solution and show that vanishing positive-side regularization selects it. We prove uniqueness, quantitative stability, and convergence of sampled nonnegative networks under an Osgood condition on the mass near the threshold along a reference solution. Rank-one examples establish sharpness among uniqueness guarantees based only on this mass. Numerical experiments illustrate how recovery interrupts new loss transmission while past losses persist. Using the disclosed sovereign portfolios of 116 banks under prescribed stress scenarios, we also examine how the choice of retained channels affects approximation accuracy. In the baseline scenario, retaining the two most strongly shocked channels gives a maximum buffer-path error about one fifteenth that of a twelve-mode singular-value truncation.

Date: 2026-08, Revised 2026-10
New Economics Papers: this item is included in nep-net
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