Multivariate systemic risk measures and computation by deep learning algorithms
提出了基于深度学习的算法来计算多变量效用函数定义的系统性短缺风险度量，讨论了公平性属性，并通过基准模型验证了算法的收敛性。
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 in which explicit formulas are not available.