箱约束的联合估计-鲁棒性投资组合选择问题  

Portfolio selection by joint estimation and robustness optimization with a box constraint

作　　者：王英晓 孔令臣[1] Yingxiao Wang;Lingchen Kong

机构地区：[1]北京交通大学数学与统计学院,北京100044

出　　处：《中国科学:数学》2025年第2期323-342,共20页Scientia Sinica:Mathematica

基　　金：国家自然科学基金(批准号:12071022)资助项目。

摘　　要：投资组合优化问题中的输入参数大多是由历史数据估计而来,估计的不确定性可能对Markowitz投资组合模型产生巨大的影响.近期,一个联合估计与鲁棒性的优化框架(joint estimation and robustness optimization,JERO)被提出,通过结合参数估计和优化问题以减弱估计不确定性对优化问题的影响.JERO框架被应用到投资组合优化领域(JERO with the mean return and the risk(variance)constraints,JERO-MV),同时考量了投资组合模型中有价值的两个度量:投资组合的回报和风险.但该模型可能会导致投资组合过分集中于某几个资产,这将增加投资风险和成本.本文在JERO-MV模型的基础上增加分散化约束,并给出该模型的可行性条件.本文在真实数据集上进行了大量的数值实验,并与JERO-MV模型进行对比.在大多数情形下,我们的模型都有更好的样本外表现.Most of the input parameters in portfolio optimization problems are estimated from historical data.The uncertainty of the estimation may have a huge impact on the Markowitz portfolio model.Recently,a joint estimation and robustness optimization(JERO)framework,which can mitigate estimation uncertainty in optimization problems by incorporating both the parameter estimation and the optimization problem,was proposed.The JERO framework is applied to the portfolio optimization problem and it simultaneously contains two valuable measures of the portfolio model:the mean return and the risk(variance)of a portfolio.This model is referred to as JERO-MV.However,the JERO-MV model may lead to portfolios that are highly concentrated on a few assets.In this paper,we combine the JERO-MV model with the diversification constraints by adding the constraints on the asset weights.The feasibility conditions of our model are also given.We conduct extensive numerical experiments on real data sets and compare the results with the JERO-MV model.In most cases,our models have better out-of-sample performances.

关 键 词：投资组合优化 参数估计 联合估计和鲁棒性 分散化约束 

分 类 号：F831.51[经济管理—金融学] O224[理学—运筹学与控制论]