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.

在这项工作中，我们提出了基于深度学习的算法，用于计算通过多元效用函数定义的系统性短缺风险度量。我们讨论关键的相关理论方面，特别关注原始最优的公平性和相关的风险分配。我们提供的算法允许学习原始优化器、对偶表示的最优值以及相应的公平风险分配。我们通过与基于配对指数效用函数的基准模型进行比较来测试我们的算法，我们可以为此提供明确的公式。我们还展示了在没有明确公式的情况下收敛的证据。