中文摘要：

建立了具有交易成本和交易量限制的多阶段均值-绝对偏差投资组合模型,并利用离散近似迭代法对其进行求解。离散近似迭代法的基本思路是：将连续型状态变量离散化,根据网络图的构造方法将组合模型转化为多阶段赋权有向图;运用极大代数求出起点至终点的最长路程,获得模型的一个可行解;以可行解为基础,继续迭代直至前后两个可行解非常接近。证明了离散近似迭代法的收敛性、复杂性和线性收敛,并通过实证验证了其算法的有效性。

英文摘要：

This paper proposes a model for multistage mean-absolute deviation portfolio selection with constraints on transaction cost and trade volume,and uses the discrete approximate iteration method for its solution.First,the state variables are discretized and the model is transformed into multistage weighted digraph according to the network method.Secondly,max-plus algebra is employed to solve the maximal path that is the admissible solution.Finally,based on the admissible solution,iterating is conducted until the two admissible solutions are close.The convergence,complexity and linear convergence of the proposed method are proved,and the algorithm is confirmed efficient by empirical research.