基于离散近似迭代法的多阶段M-SAD投资组合优化

Discrete Approximate Iteration Method on the Mean-semi-absolute Deviation Multiperiod Portfolio Selection

提出了具有交易成本和交易量限制的多阶段均值-半绝对偏差(M-SAD)投资组合模型,并用自创算法——离散近似迭代方法求解。该算法的基本思路为:首先,将连续型状态变量离散化,根据网络图的构造方法将上述模型转化多阶段赋权有向图;其次,运用嘉量原理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,继续迭代直到前后两个可行解非常接近。文章还证明了该方法的收敛性和复杂性。

The muhiperiod mean-semi-absolute deviation portfolio selection model is proposed with the transaction costs and the constrainted on trade volumes and used special algorithm-the discrete approximate iteration method to solve it. Firstly, according to the network method, discretizes the state variables and transforms the model into multiperiod weighted digraph;Secondly, uses Jar-metric principle 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 and complex of the method are also proved.