现有的多阶段投资组合优化问题普遍利用动态规划方法来进行求解, 然而对 于较为复杂的优化问题而言, 该方法并不适用. 针对此类复杂投资组合优化问题, 文章首先在广义的多阶段均值-方差理论框架下, 构建一类存在凸锥约束的投资组合优化模型. 进而提出了一种有效的线性反馈策略, 通过计算投资组合在各阶段财富值的收益和风险值, 可将该动态随机控制问题转化为一个传统的凸优化问题. 最后, 在开环和闭环两种策略形式下通过数值仿真验证文章所提出反馈策略的有效性. 结果表明, 所提出的开环策略占优于已有的开环策略, 且能够有效地拟合由动态规划所得精确投资策略.

The existing multi-period portfolio optimization problems usually use dynamic programming approach to obtain the feedback investment strategy. However, this method may not work for some complex optimization problems. To address these problems, we construct a generalized multi-period mean-variance portfolio optimization model with convex cone constraints. We also propose an effective linear feedback strategy to deal with this problem. Then, the expected returns and risks of portfolio at each period can be calculated, and the dynamic stochastic control problem can be transformed into a traditional convex optimization problem. Finally, some numerical simulations are used to verify the effectiveness of the open-loop and closed-loop strategies. The results indicate that: (i) The performance of this proposed open-loop strategy always outperforms that of the traditional open-loop strategy; (ii) This proposed linear feedback strategy can effectively fit the optimal investment strategy obtained by dynamic programming approach.