Computing Systemic Risk Measures with Graph Neural Networks
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| Format: | Preprint |
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2024
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| _version_ | 1866909842670616576 |
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| author | Gonon, Lukas Meyer-Brandis, Thilo Weber, Niklas |
| author_facet | Gonon, Lukas Meyer-Brandis, Thilo Weber, Niklas |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_07222 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Computing Systemic Risk Measures with Graph Neural Networks Gonon, Lukas Meyer-Brandis, Thilo Weber, Niklas Computational Finance Machine Learning Mathematical Finance 68T07, 91G45, 91G60, 91G70 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. |
| title | Computing Systemic Risk Measures with Graph Neural Networks |
| topic | Computational Finance Machine Learning Mathematical Finance 68T07, 91G45, 91G60, 91G70 |
| url | https://arxiv.org/abs/2410.07222 |