求解一类投资组合问题的鲁棒镜像下降SA方法  

Robust mirror descent SA method solving a class of portfolio problems

作　　者：王炜[1] 王丹丹 李三硕 WANG Wei;WANG Dandan;LI Sanshuo(School of Mathematics, Liaoning Normal University, Dalian 116029, China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《辽宁师范大学学报（自然科学版）》2021年第1期1-6,共6页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11671184);辽宁省教育厅科学技术研究项目(LJ2019005)。

摘　　要：随着经济的发展,投资组合越来越受到人们的关注,其主要研究如何在风险范围确定的情况下设计合理的优化方案,可以帮助投资者获得最多的利润.然而在实际投资问题中,许多不确定因素会影响投资收益,如何选取有效的投资组合方案规避一些不确定因素的影响很关键.因此在投资组合模型中引入随机变量来处理可以得到有效的投资方案.目前,对含有随机变量的投资组合问题的求解方法有很多,使用鲁棒镜像下降SA方法(简称RMDSA)去求解这一问题,并对所用的方法做出收敛性分析,说明其有效性.With the development of economy,more and more people pay attention to the portfolio problem,which mainly studies how to design a reasonable optimization scheme when the risk range is certain,in order to help investors to get the most profits.However,many uncertain factors affect the profits in the actual portfolio problems,and it is crucial to choose an effective portfolio scheme to avoid the effect of some uncertainties.Therefore,introducing random variables into the portfolio model can get effective investment schemes.So far,there are many ways to solve the portfolio problem with random variables,the writers use robust mirror descent SA method(RMDSA)to solve the problem.The convergence analysis of the method used is made to show its effectiveness.

关 键 词：投资组合问题 鲁棒镜像下降SA方法 随机优化 

分 类 号：O221.5[理学—运筹学与控制论]