# Deep Learning for Systemic Risk Measures

arXiv: https://arxiv.org/abs/2207.00739 · HTML: https://mlsanity.com/paper/2207.00739/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 29 references that are in the map.
- First posted on arXiv 2 Jul 2022.

## Builds on (most cited first, 7 of 7)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Sig-Wasserstein GANs for Time Series Generation](https://mlsanity.com/paper/2111.01207/) (2021)
- [Deep Hedging: Learning to Simulate Equity Option Markets](https://mlsanity.com/paper/1911.01700/) (2019)
- [Deep Learning in Finance](https://mlsanity.com/paper/1602.06561/) (2016)
- [Deep Fictitious Play for Stochastic Differential Games](https://mlsanity.com/paper/1903.09376/) (2019)
- [Signatured Deep Fictitious Play for Mean Field Games with Common Noise](https://mlsanity.com/paper/2106.03272/) (2021)
- [Connecting GANs, MFGs, and OT](https://mlsanity.com/paper/2002.04112/) (2020)

## Built on by (most cited first, 3 of 3)

- [Computing Systemic Risk Measures with Graph Neural Networks](https://mlsanity.com/paper/2410.07222/) (2024)
- [Multivariate Systemic Risk Measures and Computation by Deep Learning Algorithms](https://mlsanity.com/paper/2302.10183/) (2023)
- [TRUST-SCF: Transformer-based Risk Understanding and Scoring for Transactional Supply Chain Finance](https://mlsanity.com/paper/2606.08140/) (2026)

## Abstract (arXiv)

The aim of this paper is to study a new methodological framework for systemic risk measures by applying deep learning method as a tool to compute the optimal strategy of capital allocations. Under this new framework, systemic risk measures can be interpreted as the minimal amount of cash that secures the aggregated system by allocating capital to the single institutions before aggregating the individual risks. This problem has no explicit solution except in very limited situations. Deep learning is increasingly receiving attention in financial modelings and risk management and we propose our deep learning based algorithms to solve both the primal and dual problems of the risk measures, and thus to learn the fair risk allocations. In particular, our method for the dual problem involves the training philosophy inspired by the well-known Generative Adversarial Networks (GAN) approach and a newly designed direct estimation of Radon-Nikodym derivative. We close the paper with substantial numerical studies of the subject and provide interpretations of the risk allocations associated to the systemic risk measures. In the particular case of exponential preferences, numerical experiments demonstrate excellent performance of the proposed algorithm, when compared with the optimal explicit solution as a benchmark.