论文标题
一类数据驱动的分配稳健风险度量的紧密界限
Tight Bounds for a Class of Data-Driven Distributionally Robust Risk Measures
论文作者
论文摘要
本文扩大了强大的力矩问题的概念，以使用瓦斯坦斯坦距离作为歧义度量来结合分布歧义。研究了一维经典的Chebyshev-Cantelli（零部分时刻）的不平等，围巾和LO（第一部分时刻）的界限和一维半偏见（第二部分时刻）。制定了无限的尺寸原始问题，并得出了更简单的有限维二重要问题。一个主要的激励问题是数据驱动的分布歧义如何影响力矩的界限。为了回答这个问题，开发了一些理论，并为库存控制和投资组合管理中的特定问题实例进行了计算实验。最后，讨论了一些未来研究的开放问题和建议。
This paper expands the notion of robust moment problems to incorporate distributional ambiguity using Wasserstein distance as the ambiguity measure. The classical Chebyshev-Cantelli (zeroth partial moment) inequalities, Scarf and Lo (first partial moment) bounds, and semideviation (second partial moment) in one dimension are investigated. The infinite dimensional primal problems are formulated and the simpler finite dimensional dual problems are derived. A principal motivating question is how does data-driven distributional ambiguity affect the moment bounds. Towards answering this question, some theory is developed and computational experiments are conducted for specific problem instances in inventory control and portfolio management. Finally some open questions and suggestions for future research are discussed.
