# Multivariate Systemic Risk Measures and Computation by Deep Learning Algorithms

arXiv: https://arxiv.org/abs/2302.10183 · HTML: https://mlsanity.com/paper/2302.10183/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 21 references that are in the map.
- First posted on arXiv 2 Feb 2023.

## Builds on (most cited first, 5 of 5)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [A Neural Network Approach for High-Dimensional Optimal Control Applied to Multi-Agent Path Finding](https://mlsanity.com/paper/2104.03270/) (2021)
- [Signatured Deep Fictitious Play for Mean Field Games with Common Noise](https://mlsanity.com/paper/2106.03272/) (2021)
- [Deep Learning for Systemic Risk Measures](https://mlsanity.com/paper/2207.00739/) (2022)
- [Deep Learning the Efficient Frontier of Convex Vector Optimization Problems](https://mlsanity.com/paper/2205.07077/) (2022)

## Built on by (most cited first, 1 of 1)

- [Computing Systemic Risk Measures with Graph Neural Networks](https://mlsanity.com/paper/2410.07222/) (2024)

## Abstract (arXiv)

In this work we propose deep learning-based algorithms for the computation of systemic shortfall risk measures defined via multivariate utility functions. We discuss the key related theoretical aspects, with a particular focus on the fairness properties of primal optima and associated risk allocations. The algorithms we provide allow for learning primal optimizers, optima for the dual representation and corresponding fair risk allocations. We test our algorithms by comparison to a benchmark model, based on a paired exponential utility function, for which we can provide explicit formulas. We also show evidence of convergence in a case for which explicit formulas are not available.