Multivariate Systemic Risk Measures and Computation by Deep Learning Algorithms

• URL: http://arxiv.org/abs/2302.10183v2
• Date: Wed, 14 Jun 2023 19:19:36 GMT
• Title: Multivariate Systemic Risk Measures and Computation by Deep Learning Algorithms
• Authors: Alessandro Doldi, Yichen Feng, Jean-Pierre Fouque, Marco Frittelli
• Abstract summary: 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 primals, optima for the dual representation and corresponding fair risk allocations.
• Score: 63.03966552670014
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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