一种高阶牛顿法求解投资组合优化模型  

High Order Newton’s Method for Portfolio Optimization Model

作　　者：雍龙泉[1] YONG Long-quan(School of Mathematics and Computer Science,Shaanxi University of Technology,Hanzhong 723001,China)

机构地区：[1]陕西理工大学数学与计算机科学学院

出　　处：《数学的实践与认识》2019年第19期216-221,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11401357);陕西省青年科技新星项目(2016KJXX-95);陕西省教育厅科研项目(17JK0146);陕西理工大学科研项目(SLGKY2017-05)

摘　　要：建立了均值方差投资组合优化模型.通过把凸二次规划转化为非光滑的非线性方程组,并对其光滑化处理,进而转化为光滑非线性方程组,再用高阶牛顿法进行求解.最后应用于投资组合优化模型,通过改变年收益率而得到不同的投资决策.该算法计算速度快,效率高,因此算法具有较广泛的应用空间.Portfolio optimization model is established.Then we transform the convex quadratic programming model into nonsmooth nonlinear equations,and smooth it by smoothing approximation function,thus we obtain smooth nonlinear equations,which can be solved by high order Newton’s method.Finally this method is applied to the portfolio optimization model,and by changing the yields we get different investment decisions.This method has a high computation speed and computational efficiency,so it has a broad application space.

关 键 词：投资组合优化模型 凸二次规划 非线性方程组 高阶牛顿法 

分 类 号：G63[文化科学—教育学]