多阶段均值-平均绝对偏差投资组合的离散近似迭代法  

Discrete Approximate Iteration Method On the Mean-Absolute Deviation Multiperiod Portfolio Selection and the Empirical Research

作　　者：张鹏[1] 

机构地区：[1]武汉科技大学管理学院,武汉430081

出　　处：《系统管理学报》2010年第3期266-271,共6页Journal of Systems & Management

基　　金：教育部人文社科研究项目(08JC630062);湖北省教育厅人文社科研究项目(2008q115);武汉科技大学校基金项目(2008XY33)

摘　　要：提出了具有交易成本和交易量限制的多阶段均值-平均绝对偏差投资组合模型,并用离散近似迭代法求解。该算法的基本思路为:首先,连续型状态变量离散化,将上述模型转化为多阶段赋权有向图;其次,运用极大代数求出起点至终点的最长路程,即获得模型的一个可行解;最后,以该可行解为基础,继续迭代直到前后2个可行解非常接近。证明了该方法的收敛性、线性收敛和复杂性。最后,通过实证研究验证了算法的有效性。The paper proposed the multiperiod mean-average absolute deviation portfolio selection model with the transaction costs and the constraints on trade volumes and used the new algorithm—the discrete approximate iteration method to solve it. Firstly,according to the network method,it discretizes the state variables and transforms the model into multiperiod weighted digraph;Secondly,it uses max-plus algebra to solve the maximal path that is the admissible solution;At last, continues iterating until the two admissible solution is near based on the admissible solution.The convergence,linear convergence and complex of the method paper are proved.The algorithms were proved efficient by the empirical research.

关 键 词：多阶段投资组合 均值-平均绝对偏差 离散近似迭代法 极大代数 旋转算法 

分 类 号：F224.9[经济管理—国民经济] O221.2[理学—运筹学与控制论]