Multivariate Systemic Risk Measures and Computation by Deep Learning Algorithms

TL;DR

This paper introduces deep learning algorithms to compute multivariate systemic risk measures, focusing on theoretical properties and demonstrating convergence and accuracy through benchmark comparisons.

Contribution

It presents novel deep learning algorithms for calculating systemic risk measures and risk allocations, with theoretical analysis and empirical validation.

Findings

Algorithms successfully learn primal optimizers and risk allocations

Convergence demonstrated even without explicit formulas

Comparison with benchmark model validates accuracy

Abstract

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.