# Computing Systemic Risk Measures with Graph Neural Networks

arXiv: https://arxiv.org/abs/2410.07222 · HTML: https://mlsanity.com/paper/2410.07222/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 75 references that are in the map.
- First posted on arXiv 30 Sep 2024.

## Builds on (most cited first, 16 of 16)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [A Review on Graph Neural Network Methods in Financial Applications](https://mlsanity.com/paper/2111.15367/) (2021)
- [Generalization Analysis of Message Passing Neural Networks on Large Random Graphs](https://mlsanity.com/paper/2202.00645/) (2022)
- [Mapping Images to Scene Graphs with Permutation-Invariant Structured Prediction](https://mlsanity.com/paper/1802.05451/) (2018)
- [On the approximation capability of GNNs in node classification/regression tasks](https://mlsanity.com/paper/2106.08992/) (2021)
- [Probabilistic Bisection Converges Almost as Quickly as Stochastic Approximation](https://mlsanity.com/paper/1612.03964/) (2016)
- [Systemic risk analysis in reconstructed economic and financial networks](https://mlsanity.com/paper/1411.7613/) (2014)
- [Computation of systemic risk measures: a mixed-integer programming approach](https://mlsanity.com/paper/1903.08367/) (2019)
- [Deep Learning for Systemic Risk Measures](https://mlsanity.com/paper/2207.00739/) (2022)
- [Enhanced reconstruction of weighted networks from strengths and degrees](https://mlsanity.com/paper/1307.2104/) (2013)
- [Multivariate Systemic Risk Measures and Computation by Deep Learning Algorithms](https://mlsanity.com/paper/2302.10183/) (2023)

## Built on by (most cited first, 3 of 3)

- [DeXposure-FM: A Time-series, Graph Foundation Model for Credit Exposures and Stability on Decentralized Financial Networks](https://mlsanity.com/paper/2602.03981/) (2026)
- [Explainable Graph Neural Networks for Interbank Contagion Surveillance: A Regulatory-Aligned Framework for the U.S. Banking Sector](https://mlsanity.com/paper/2604.14232/) (2026)
- [SCAFDS: Edge-Feature Graph Attention for Interbank Fraud Detection with Attribution-Grounded SAR Generation](https://mlsanity.com/paper/2605.18913/) (2026)

## Abstract (arXiv)

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.