CVaR鲁棒均值-CVaR投资组合模型与求解

doi:10.15960/j.cnki.issn.1007-6093.2017.01.001

运筹学学报

• 运筹学 • 下一篇

CVaR鲁棒均值-CVaR投资组合模型与求解

康志林^1,3 李仲飞^2,*

1. 中山大学数学学院, 广州 510275; 2. 中山大学管理学院, 广州 510275; 3. 华侨大学数学科学学院, 福建泉州 362021

收稿日期:2016-09-14 出版日期:2017-03-15 发布日期:2017-03-15
通讯作者: 李仲飞 lnslzf@mail.sysu.edu.cn
基金资助:
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)

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

KANG Zhilin^1,3 LI Zhongfei^2,*

1. School of Mathematics, Sun Yat-sen University, Guangzhou 510275, China; 2. Sun Yat-sen Business School, Sun Yat-sen University, Guangzhou 510275, China; 3. School of Mathematical Science, Huaqiao University, Quanzhou 362021, Fujian, China

Received:2016-09-14 Online:2017-03-15 Published:2017-03-15

摘要/Abstract

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.

关键词: 组合证券投资, CVaR鲁棒, 对偶法, 光滑化, 重采样

Abstract:

When calculating the optimal portfolios, the traditional mean-risk (including variance, value-at-risk (VaR), conditional value at risk (CVaR)) optimization model often assumes that mean returns are known constant values. In actual asset allocation, 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.

Key words: portfolio selection, CVaR robust, dual method, smoothing method, resampling

康志林, 李仲飞. CVaR鲁棒均值-CVaR投资组合模型与求解[J]. 运筹学学报, doi: 10.15960/j.cnki.issn.1007-6093.2017.01.001.

KANG Zhilin, LI Zhongfei. CVaR robust mean-CVaR portfolio optimization model and the solving methods[J]. Operations Research Transactions, doi: 10.15960/j.cnki.issn.1007-6093.2017.01.001.

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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

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