Computing Systemic Risk Measures with Graph Neural Networks

ArXiv ID: 2410.07222 “View on arXiv”

Authors: Unknown

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.

Keywords: systemic risk, financial networks, graph neural networks, Eisenberg-Noe model, permutation equivariance, financial systems

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper utilizes advanced mathematical concepts including stochastic analysis, graph theory, convex optimization, and theoretical properties of neural networks (universal approximation, permutation equivariance), which drives the high math complexity score. While it includes a dedicated ‘Numerical Experiments’ section with empirical comparisons, the methodology is primarily algorithmic and relies on synthetic/idealized network simulations rather than real-market data pipelines, placing it in the high-math, high-rigour quadrant.

  flowchart TD
    A["Research Goal:<br>Compute Systemic Risk<br>for Financial Networks"] --> B["Input Data:<br>Stochastic Bilateral Liabilities<br>& Graph Structure"]
    B --> C["Methodology:<br>Extend Systemic Risk Measures<br>using Graph Neural Networks"]
    C --> D["Core Process:<br>Eisenberg-Noe Market Clearing<br>with Permutation Equivariance"]
    D --> E["Optimization:<br>Find Minimal Bailout Capital<br>& Optimal Random Allocation"]
    E --> F["Comparison:<br>vs. Benchmark Allocations"]
    F --> G["Key Findings:<br>GNNs & (X)PENNs Outperform<br>Other Approaches"]