CVaR鲁棒均值-CVaR投资组合模型与求解  

CVaR robust mean-CVaR portfolio optimization model and the solving methods

作　　者：康志林[1,2] 李仲飞[3] 

机构地区：[1]中山大学数学学院,广州510275 [2]华侨大学数学科学学院,福建泉州362021 [3]中山大学管理学院,广州510275

出　　处：《运筹学学报》2017年第1期1-12,共12页Operations Research Transactions

基　　金：国家自然科学基金重点项目(No.71231008);福建省中青年教师教育科研项目(No.JA15041);广东省自然科学基金团队项目(No.2014A030312003)

摘　　要：传统的均值-风险(包括方差、VaR、CVaR等)组合选择模型在计算最优投资组合时,常假定均值是已知的常值,但在实际资产配置中,收益的均值估计会有偏差,即存在着估计风险.在利用CVaR测度估计风险的基础上,研究了CVaR鲁棒均值-CVaR投资组合选择模型,给出了另外两种不同的求解方法,即对偶法和光滑优化方法,并探讨了它们的相关性质及特征,数值实验表明在求解大样本或者大规模投资组合选择问题上,对偶法和光滑优化方法在计算上是可行且有效的.When calculating the optimal portfolios, the traditional mean-risk （in- cluding variance, value-at-risk （VaR）, conditional value at risk （CVaR）） optimization model often assumes that mean returns are known constant values. In actual asset al- location, however, estimation of mean return will have deviation, namely there exists risk of estimation. On the basis of estimating the risk measured by CVaR, this paper further studies CVaR robust mean-CVaR portfolio optimization model and presents two different optimization algorithms, namely, the dual method and the smoothing method. Moreover, we explore some properties and characteristics of the two methods. Finally, we give some numerical experiments to show the feasibility and effectiveness of these two methods.

关 键 词：组合证券投资 CVaR鲁棒 对偶法 光滑化 重采样 

分 类 号：F830.9[经济管理—金融学] O224.0[理学—运筹学与控制论]