Low-Rank and Graphon Limits for Dynamic Threshold Distress Contagion in Heterogeneous Financial Networks

Battle Count: 50

This paper is primarily about systemic risk modeling and financial network theory rather than trading strategies. It provides tools for understanding contagion dynamics and network vulnerability, which could inform risk management overlays in portfolio construction. The low-rank factorization approach could potentially be adapted for exposure decomposition in multi-asset portfolios, but the paper does not address trading signals, execution, or alpha generation directly.

The theoretical framework involves advanced mathematical tools: Wasserstein stability analysis, Osgood comparison theorems, VC-subgraph empirical process bounds, Picard iteration in function spaces, transport PDEs, and graphon theory. Numerical implementation requires solving coupled nonlinear ODE systems with threshold indicators, handling solution selection via regularization ramps, and constructing factor decompositions from real data. The proofs span over 60 pages. However, the reduced K-dimensional feedback system is computationally tractable (O(NK) vs O(N^2)), and the numerical experiments use standard explicit Euler methods.

The paper provides supplementary scripts for the Osgood experiment, six-bank calculations, and piecewise-smooth/30-mode graphon experiments. However, Gaussian-mixture parameter files, complete directedness settings, the EBA extract, and full-sample processing/simulation scripts are explicitly stated as not included in the archive. The mathematical proofs are self-contained, and numerical parameters (time steps, grid sizes, factor loadings) are specified in detail. The EBA data source is publicly available.