AI 中文总结
该研究针对异质金融网络提出动态阈值困境传染的低秩与图极限模型，建立约化动力学的稳定性与适定性，结合EBA透明度测试示例验证了重采样误差的理论尺度。
AI 中文摘要
我们研究了一个针对大型金融机构群体的确定性传染模型，这些机构通过加权有向敞口矩阵相连。该模型的符号约定与损失项源于带部分恢复和利息偿付的违约级联，而动态模型通过占用时间记录困境，因此允许恢复。秩为K的分解可将有限网络精确约化为K个宏观反馈坐标。对于有界Lipschitz损失，约化动力学构成非自治K维常微分方程；我们证明了其关于类型律的Wasserstein稳定性，并推导了联合状态-因子分布的传输表示。在固定潜空间上，相关的有向核方程适定且L¹稳定，定量桥定理将有限总体误差与核近似误差分离。对于指示损失，我们在阈值正则性下建立了固定秩适定性，并对采样解的可测选择得到了Vapnik-Chervonenkis型估计。在图on（图子）层面，我们证明了因子化核及满足均匀横截性的分段C¹核-轮廓对的适定性，以及均匀横截近似族的扰动定理。基于2025年欧洲银行管理局（EBA）透明度测试的主权重叠示例，从公开披露计算了因子载荷和先验敏感性界；对经验117家银行总体的重采样误差与预测的N⁻¹/²尺度一致。
英文摘要
The transmission of financial distress depends on the structure of exposures, the distribution of institutional buffers, and the duration of stress. We develop a dynamic model in which losses flow through weighted directed networks while counterparties are distressed, with recovery and repeated threshold crossings incorporated into the same system. A representation with \(K\) exposure factors closes the \(N\)-institution dynamics through \(K\) feedback coordinates, preserving heterogeneous sender and receiver roles. For bounded Lipschitz losses, Wasserstein stability and aligned \(L^1\) kernel estimates connect finite populations, factor models, and directed-kernel limits, with separate bounds for sampling and exposure approximation. For the hard threshold, every bounded nonnegative kernel admits a greatest cumulative-distress solution selected by vanishing positive-side regularization. The mass of institutions near the threshold governs stability: an Osgood condition along one reference path yields uniqueness, quantitative perturbation bounds, and convergence under sampled latent labels. Rank-one examples establish sharpness among uniqueness criteria based on threshold-layer mass, and a branchwise condition verifies the regularity directly from the initial profile and kernel. Numerical experiments examine how network structure and threshold concentration affect the dynamics. An application to disclosed EBA sovereign holdings constructs common-exposure factors and quantifies sensitivity to portfolio perturbations.
