Year: 2026
Type: article
Abstract: . This paper investigates systemic risk measures for stochastic financial networks of explicitly modeled bilateral liabilities. We extend the notion of systemic risk measures based on random allocations from Biagini, Fouque, Fritelli, and Meyer-Brandis (2019) to graph structured data. In particular, we focus on aggregation functions that are 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 then study numerical methods for the approximation of systemic risk and optimal random allocations. Our proposition is to use permutation-equivariant architectures of neural networks such as graph neural networks (GNNs) and a class that we name (extended) permutation-equivariant neural networks ((X)PENNs). The performance of these architectures is benchmarked against several alternative allocation methods. 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.
DOI: 10.1137/24m1697402
Authors: Lukas Gonon, Thilo Meyer-Brandis, Niklas Weber
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W4403363700