Low-rank and graphon limits for dynamic threshold distress contagion in heterogeneous financial networks
Pengbin Feng
Abstract
We study a deterministic contagion model for a large population of financial institutions connected by a weighted directed exposure matrix. The sign convention and loss term are motivated by a default cascade with partial recovery and interest servicing, whereas the dynamic model records distress through occupation time and therefore permits recovery. A rank-\(K\) factorization yields an exact reduction of the finite network to \(K\) macroscopic feedback coordinates. For bounded Lipschitz losses, the reduced dynamics form a nonautonomous \(K\)-dimensional ODE; we prove Wasserstein stability with respect to the type law and derive a transport representation for the joint state--factor distribution. On a fixed latent space, the associated directed-kernel equation is well posed and \(L^1\)-stable, and a quantitative bridge theorem separates finite-population error from kernel-approximation error. For the indicator loss, we establish fixed-rank well-posedness under threshold regularity and a Vapnik--Chervonenkis-type estimate for measurable selections of sampled solutions. At the graphon level, we prove well-posedness for factorized kernels and for piecewise-\(C^1\) kernel--profile pairs satisfying uniform transversality, together with a perturbation theorem for uniformly transverse approximation families. A sovereign-overlap illustration based on the 2025 EBA transparency exercise computes factor loadings and a priori sensitivity bounds from public disclosures; resampling errors on the empirical 117-bank population are consistent with the predicted \(N^{-1/2}\) scale.
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