具有卖空总量限制的多阶段M—SAD投资组合优化

文章提出具有卖空总量限制、阈值约束和V型交易成本的多阶段均值—半绝对偏差（M-SAD）投资组合优化模型。该模型分别运用均值和半绝对偏衡量资产的收益率和风险。由于交易成本的存在，该模型不满足无后效性的动态优化问题。文章将该模型近似为一般动态规划问题，提出一种新的离散迭代方法，并证明该算法是线性收敛的。最后，文章通过实证研究比较分析卖空总量限制和风险偏好系数取不同值时对投资组合最优策略的影响，验证模型和算法的有效性。

Multiperiod Mean Semi-absolute Deviation Portfolio Selection with Total Short Selling Constraints

In this paper, a new multiperiod mean semi-absolute deviation portfolio selection model with total short sellingconstraints, threshold constraints, transaction costs and borrowing constraints is proposed. The return and the risk are quantified by the mean value of return and by the semi-absolute deviation of return, respectively. Because of the transaction costs, the proposed model is a dynamic optimization problem with path dependence. The proposed model is approximated to a dynamic programming model. A novel discrete iteration method is designed to obtain the optimal portfolio strategy, and is proved linearly convergent.Finally, the comparison analysis of the different total short selling constraints and different preference coefficients in the portfolio is provided by numerical examples to illustrate the efficiency of the proposed method and the designed algorithm using real data from the Shanghai Stock Exchange.