投资组合优化模型的一个序列凸近似算法  

A sequential convex approximation algorithm for portfolio optimization model

作　　者：李卫国[1,2] 张宏伟[1] 梁锡军 

机构地区：[1]大连理工大学数学科学学院,辽宁大连116024 [2]辽宁地质工程职业学院,辽宁丹东118303 [3]中国石油大学(华东)理学院,山东青岛266580

出　　处：《大连理工大学学报》2017年第3期321-326,共6页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(61503412);辽宁省教育科学“十三五”规划研究项目(JG16EB101)

摘　　要：以CVaR为代表的凸优化投资组合模型近年来引起了广泛研究.为克服传统投资组合模型中凸近似的不足,提出了一个投资组合的DC规划模型.该模型用一个DC函数替代了CVaR模型中的凸近似函数,同时要求所有约束条件在概率意义下成立.进一步地,提出了一个序列凸近似(SCA)算法用于求解DC规划问题,并运用Monte-Carlo方法来实现SCA算法.初步的实验结果表明,因子收益服从"尖峰厚尾"分布时,模型的目标函数值优于采用CVaR近似的目标函数值.CVaR has drawn extensive attentions as a representative convex optimization portfolio model in recent years.To overcome the limits of convex approximations in traditional portfolio models,a DC programming model for portfolio is proposed.In the proposed programming model,a DC function is used as a surrogate for the convex approximation function in the CVaR model.All the constraints are satisfied in the probabilistic sense in the DC programming problem.Moreover,a sequential convex approximation（SCA）algorithm is designed to solve the DC programming problem.The SCA algorithm is implemented by employing Monte-Carlo method.Preliminary experimental results have shown that the objective function values of the DC programming are better than those with CVaR approximation when the income factors satisfy″high peak and fat tail″distributions.

关 键 词：投资组合 序列凸近似 凸优化 MONTE-CARLO方法 

分 类 号：O224[理学—运筹学与控制论]