Multivariate Systemic Risk Measures and Computation by Deep Learning Algorithms
This work addresses risk management in financial systems by providing computational tools for systemic risk measures, but it appears incremental as it builds on existing theoretical frameworks with new algorithmic implementations.
The authors tackled the computation of multivariate systemic shortfall risk measures using deep learning algorithms, achieving convergence in cases without explicit formulas and comparing favorably to a benchmark model with explicit solutions.
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.