Default Contagion, Matrix Approximation, and Control in Sparse Financial Networks
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866916042713858048 |
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| author | Zhang, Aoxin Wang, Yingzhe |
| author_facet | Zhang, Aoxin Wang, Yingzhe |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24833 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Default Contagion, Matrix Approximation, and Control in Sparse Financial Networks Zhang, Aoxin Wang, Yingzhe Optimization and Control Risk Management 91G40, 91G80, 60H30, 60K35, 93E20, 49L20, 05C82 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. |
| title | Default Contagion, Matrix Approximation, and Control in Sparse Financial Networks |
| topic | Optimization and Control Risk Management 91G40, 91G80, 60H30, 60K35, 93E20, 49L20, 05C82 |
| url | https://arxiv.org/abs/2605.24833 |