具有借贷限制的多阶段M-SAD投资组合决策研究

针对资产投资不允许卖空的情况,提出了具有借款限制且借贷利率相同和不同这两种条件下的多阶段均值-半绝对偏差(M-SAD)投资组合模型,该模型的优化为连续型动态规划问题。文中运用自创算法——离散近似迭代法求解,其基本思路为: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,即获得模型的一个可行解;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。文中还证明了该方法的线性收敛性和复杂性,并以一个具体实例比较了两种情况下的最优投资策略。

Multiperiod portfolio selection with borrowing and lending constraints based on the mean semi-absolute deviation

This paper proposes a multiperiod mean semi-absolute deviation portfolio selection model without short sales and with borrowing and lending risk-free assets constraints. The proposed model is a continuing dynamic programming problem. The discrete approximate iteration method is proposed to solve it,which is as follows:According to the network method, discretize the state variables and transform the model into multiperiod weighted digraph; use max-plus algebra to solve the maximal path that is the admissible solution; continue iterating until the two admissible solutions are near based on the admissible solution. The convergence and complex of the method are also proved. Finally, an example is given to illustrate the behavior of the proposed model and the designed algorithm using real data from Shanghai Stock Exchange.