We propose an end-to-end distributionally robust system for portfolio construction that integrates the asset return prediction model with a distributionally robust portfolio optimization model. We also show how to learn the risk-tolerance parameter and the degree of robustness directly from data. End-to-end systems have an advantage in that information can be communicated between the prediction and decision layers during training, allowing the parameters to be trained for the final task rather than solely for predictive performance. However, existing end-to-end systems are not able to quantify and correct for the impact of model risk on the decision layer. Our proposed distributionally robust end-to-end portfolio selection system explicitly accounts for the impact of model risk. The decision layer chooses portfolios by solving a minimax problem where the distribution of the asset returns is assumed to belong to an ambiguity set centered around a nominal distribution. Using convex duality, we recast the minimax problem in a form that allows for efficient training of the end-to-end system.

我们提出了一种用于投资组合构建的端到端分布稳健系统，该系统将资产回报预测模型与分布稳健投资组合优化模型相结合。我们还展示了如何直接从数据中学习风险承受能力参数和鲁棒性程度。端到端系统的优势在于，可以在训练期间在预测层和决策层之间传递信息，从而允许为最终任务训练参数，而不仅仅是为了预测性能。然而，现有的端到端系统无法量化和纠正模型风险对决策层的影响。我们提出的分布式稳健的端到端投资组合选择系统明确考虑了模型风险的影响。决策层通过解决极小极大问题来选择投资组合，其中假设资产回报的分布属于以名义分布为中心的模糊集。使用凸对偶性，我们以一种允许有效训练端到端系统的形式重新设计了极小极大问题。