基于分布式鲁棒优化的增强型指数追踪问题研究  

Enhanced index tracking problem based on distributed robust optimization

作　　者：李美玲 吴婷 LI Meiling;WU Ting(School of Mathematics and Statistics,Xidian University,Xi′an 710071,China)

机构地区：[1]西安电子科技大学数学与统计学院,陕西西安710071

出　　处：《纯粹数学与应用数学》2023年第3期422-436,共15页Pure and Applied Mathematics

基　　金：国家自然科学基金(12271419);陕西省自然科学基金青年项目(2023-JC-QN-0081);中央高校自由探索青年项目(XJS220706)。

摘　　要：增强型指数追踪是近十年来机构投资者一直使用的指数型基金管理策略,主要通过围绕标的指数的头寸建立追踪组合,并增加对特定风格或个股的倾斜来增加超额收益,兼顾了消极型和积极型管理策略的投资优点.本文针对该问题构建了基于三类矩信息不确定集合上的分布式鲁棒优化模型,并利用半无限对偶理论推导了模型的分布式鲁棒对等式,最终转化成半定规划的形式.最后,利用OR-Library的4个标准数据集进行实证分析.实验结果表明:本文提出的模型不仅可以获得稳定的样本外超额收益,而且具有更强的鲁棒性.Enhanced index tracking has gained signi cant popularity as an index fund management strategy among institutional investors over the past decade.It primarily involves constructing a tracking portfolio around the benchmark index and selectively tilting towards speci c styles or individual stocks in order to generate excess returns while maintaining a balance between the bene ts of both passive and active management strategies.In this paper,we develop a distributed robust optimization model based on three types of moment information perturbation sets to solve this problem.By applying semiin nite duality theory,we derive the distributed robust equivalent formulation of the model,ultimately reformulate it into a semide nite programming form.Finally,we conduct empirical analysis using four standard data sets from OR-Library.The experimental results demonstrate that our proposed model not only achieves stable out-of-sample excess returns but also exhibits stronger robustness.

关 键 词：增强型指数问题 分布式鲁棒 投资组合优化 半定规划 样本外分析 

分 类 号：O221.5[理学—运筹学与控制论] O221.2[理学—数学]