Computing Systemic Risk Measures with Graph Neural Networks
This work addresses the problem of efficiently computing systemic risk and optimal capital allocation in financial networks, which is important for financial regulators and institutions to manage and mitigate financial crises.
This paper extends systemic risk measures to graph-structured financial networks with bilateral liabilities, focusing on an aggregation function from a market clearing algorithm. It demonstrates the existence of an optimal random allocation for minimal bailout capital and proposes using Graph Neural Networks (GNNs) and (Extended) Permutation Equivariant Neural Networks ((X)PENNs) for approximation, showing their superiority over benchmark allocations in numerical experiments.
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.