Computing Systemic Risk Measures with Graph Neural Networks

2024-09-30

arXiv.org

AI Summary

This paper addresses the quantification of systemic risk and optimal allocation of bailout capital in stochastic financial networks, with explicit modeling of bilateral debt obligations. Methodologically, it integrates the Eisenberg–Noe clearing mechanism into a graph neural network (GNN) framework, proposing XPENN—a novel architecture satisfying strict permutation equivariance—thereby achieving the first theoretically consistent generalization of systemic risk measures to graph-structured data. Combining stochastic optimization with numerical approximation, the approach computes the minimal total bailout capital and its optimal stochastic allocation policy. Experiments demonstrate that XPENN substantially outperforms baseline methods across key dimensions: reduced bailout cost, enhanced robustness to network perturbations, and improved interpretability. The framework establishes a new paradigm for financial network risk assessment, balancing theoretical rigor with computational tractability.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Probabilistic Circuits and Graphical Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

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.

Problem

• Measuring systemic risk in financial networks with bilateral liabilities
• Developing graph neural networks for permutation equivariant risk assessment
• Optimizing bailout capital allocation to secure financial networks

Innovation

• Using graph neural networks for systemic risk
• Extending permutation equivariant neural network architectures
• Applying market clearing algorithm for risk aggregation