考虑交易成本，借款约束和阈值约束，文章提出了具有最小交易量限制的多阶段均值-半方差投资组合模型。该模型是具有路径依赖性的混合整数动态优化问题，还是NP完全问题。文章提出了前向动态规划方法求解。最后，通过一个算例比较不同风险约束下的最优投资策略，从而验证模型和算法的有效性。

In this paper the multi-period mean semivariance portfolio problem is dealt with minimum transaction lots considering, transaction costs, borrowing constraints and threshold constraints. In this case the problem of finding a feasible solution is NP-complete. An optimal investment policy can be generated to help investors not only achieve an optimal return, but also have a good risk control. The multi-period portfolio selection is the mix integer dynamic optimization problem with path dependence. The forward dynamic programming method is designed to obtain the optimal portfolio strategy. Finally, the comparison analysis with borrowing risk-free assets and without risk-free assets in the portfolio selection is provided by a numerical example to illustrate the efficiency of the proposed approaches and the designed algorithm.