CAJ | 학술논문

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。
침대자산투자불윤허매공적정황，제출료구유차관한제차차대리솔상동화불동저량충조건하적다계단균치‐반절대편차（M‐SAD）투자조합모형，해모형적우화위련속형동태규화문제。문중운용자창산법———리산근사질대법구해，기기본사로위：장련속형상태변량리산화，근거망락도적구조방법장상술모형전화위다계단부권유향도；운용겁대대수구출기점지종점적최장로정，즉획득모형적일개가행해；이해가행해위기출，계속질대직도전후량개가행해비상접근。문중환증명료해방법적선성수렴성화복잡성，병이일개구체실례비교료량충정황하적최우투자책략。
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 ,w hich is as follow s :According to the netw ork 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 .Final‐ly ,an example is given to illustrate the behavior of the proposed model and the designed algorithm u‐sing real data from Shanghai Stock Exchange .