用图神经网络计算金融网络的系统性风险，提升救助资本分配效率。
Computing Systemic Risk Measures with Graph Neural Networks
- 采用图神经网络和置换等变网络建模金融债务网络结构。
- 证明存在最优随机救助方案，可最小化整体救助资本需求。
- 实验表明置换等变模型在风险度量上优于传统基准方法。
本文研究显式建模双边债务关系的随机金融网络中的系统性风险度量。将Biagini et al. (2019)提出的系统性风险度量扩展至图结构数据，聚焦于基于Eisenberg和Noe（2001）市场清算算法推导出的聚合函数。我们证明了存在一个最优随机分配方案，能够以最小总救助资本保障网络稳定。研究了系统性风险与最优随机分配的数值逼近方法，提出使用置换等变神经网络架构，如图神经网络（GNNs）及我们命名的（扩展）置换等变神经网络（(X)PENNs）。这些模型对底层图数据具有置换等变性。数值实验显示，置换等变方法在性能上显著优于多种基准分配策略。
原文摘要 · Abstract (English)
This paper investigates systemic risk measures for stochastic financial networks of explicitly modelled bilateral liabilities. We extend the notion of systemic risk measures from Biagini, Fouque, Fritelli and Meyer-Brandis (2019) to graph structured data. In particular, we focus on an aggregation function that is derived from a market clearing algorithm proposed by Eisenberg and Noe (2001). In this setting, we show the existence of an optimal random allocation that distributes the overall minimal bailout capital and secures the network. We study numerical methods for the approximation of systemic risk and optimal random allocations. We propose to use permutation equivariant architectures of neural networks like graph neural networks (GNNs) and a class that we name (extended) permutation equivariant neural networks ((X)PENNs). We compare their performance to several benchmark allocations. The main feature of GNNs and (X)PENNs is that they are permutation equivariant with respect to the underlying graph data. In numerical experiments we find evidence that these permutation equivariant methods are superior to other approaches.
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