Abstract:We study systemic default contagion in sparse financial networks and develop a framework for deciding when aggregate exposure matrices are reliable and when node-level network information changes tail risk and control design. The first contribution is a multi-population McKean-Vlasov foundation for distance-to-default dynamics with common noise, bounded state-dependent killing, loss feedback, sparse weighted exposures, and regulatory intervention, including quantitative convergence, propagation of chaos, stability in contagion matrices, controlled well-posedness, a two-population HJB characterization, and a steep-killing bridge to absorbing-boundary contagion. The second contribution is a set of computable matrix-approximation diagnostics: finite-grid bounds driven by row-exposure dispersion and square-edge spread, constructive tail-loss gaps for networks sharing the same aggregate matrix, and a spectral-radius criterion for local cascade onset. The third contribution is an information-value theory for control, showing that node-level graph pressure has strictly positive value when within-type pressure variation interacts with nonsaturated marginal killing reduction. Matched sparse-graph and matrix experiments, common-noise tests, HJB feedback diagnostics, fixed-budget control comparisons, and EBA/Pillar 3-calibrated synthetic networks validate the framework. The main conclusion is that finite-type matrices are effective in regular-mixing regimes, whereas concentrated sparse exposures generate tail-risk and intervention effects that require local-pressure diagnostics and network-aware control.
| Comments: | Full paper with supplementary material |
| Subjects: | Optimization and Control (math.OC); Risk Management (q-fin.RM) |
| MSC classes: | 91G40, 91G80, 60H30, 60K35, 93E20, 49L20, 05C82 |
| Cite as: | arXiv:2605.24833 [math.OC] |
| (or arXiv:2605.24833v1 [math.OC] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24833 arXiv-issued DOI via DataCite (pending registration) |
From: Aoxin Zhang [view email]
[v1]
Sun, 24 May 2026 02:57:47 UTC (1,548 KB)
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