This paper develops a continuous functional framework for analyzing contagion dynamics in financial networks, extending the Navier-Stokes-based approach to network-structured spatial processes. We model financial distress propagation as a diffusion process on weighted networks, deriving a network diffusion equation from first principles that predicts contagion decay depends on the network's algebraic connectivity through the relation $\kappa = \sqrt{\lambda_2/D}$, where $\lambda_2$ is the second-smallest eigenvalue of the graph Laplacian and $D$ is the diffusion coefficient. Applying this framework to European banking data from the EBA stress tests (2018, 2021, 2023), we estimate interbank exposure networks using maximum entropy methods and track the evolution of systemic risk through the COVID-19 crisis. Our key finding is that network connectivity declined by 45\% from 2018 to 2023, implying a 26\% reduction in the contagion decay parameter. Difference-in-differences analysis reveals this structural change was driven by regulatory-induced deleveraging of systemically important banks, which experienced differential asset reductions of 17\% relative to smaller institutions. The networks exhibit lognormal rather than scale-free degree distributions, suggesting greater resilience than previously assumed in the literature. Extensive robustness checks across parametric and non-parametric estimation methods confirm declining systemic risk, with cross-method correlations exceeding 0.95. These findings demonstrate that post-COVID-19 regulatory reforms effectively reduced network interconnectedness and systemic vulnerability in the European banking system.

翻译：本文构建了一个连续泛函框架来分析金融网络中的传染动力学，将基于纳维-斯托克斯的方法拓展至网络结构的空间过程。我们将财务困境传播建模为加权网络上的扩散过程，从基本原理推导出网络扩散方程，该方程预测传染衰减取决于网络的代数连通性，其关系为 $\kappa = \sqrt{\lambda_2/D}$，其中 $\lambda_2$ 是图拉普拉斯矩阵的第二小特征值，$D$ 是扩散系数。将此框架应用于欧洲银行业管理局压力测试（2018、2021、2023年）的欧洲银行业数据，我们使用最大熵方法估计银行间风险敞口网络，并通过COVID-19危机追踪系统性风险的演变。我们的核心发现是：从2018年到2023年，网络连通性下降了45%，这意味着传染衰减参数降低了26%。双重差分分析表明，这一结构性变化是由监管驱动的系统重要性银行去杠杆化所导致的，这些银行相对于较小机构的资产降幅差异达到17%。网络呈现出对数正态而非无标度的度分布，表明其韧性比文献中先前假设的更强。在参数化和非参数化估计方法中进行的大量稳健性检验均证实了系统性风险的下降，跨方法相关性超过0.95。这些发现表明，后COVID-19时代的监管改革有效降低了欧洲银行体系的网络互连性与系统性脆弱性。