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考虑借款限制、交易量限制、交易成本和风险控制,本文提出了多阶段均值-熵投资组合模型。在该模型中,收益水平和风险分别用可能性均值和熵度量。熵值越小,投资组合包含的不确定性越低,投资组合的安全性越高。此外,熵不依赖于证券收益的对称分布。运用可能性理论,将该模型转化为显示的非线性动态优化问题。由于投资过程存在交易成本,上述模型为具有路径依赖性的动态优化问题。文章提出了前向动态规化方法求解。最后,通过实证研究比较了不同熵的取值投资组合最优投资比例和最终财富的变化,并验证了模型和算法的有效性。
Considering loan limits, trading volume constraints, transaction costs and risk control, this paper proposes a multi-stage mean-entropy portfolio model. In this model, the level and risk of return are measured by means of likelihood and entropy, respectively. The smaller the entropy, the lower the uncertainty contained in the portfolio and the more secure the portfolio. In addition, entropy does not depend on the symmetrical distribution of returns on securities. Using the possibility theory, the model is transformed into the nonlinear dynamic optimization problem. Because of the transaction costs in the investment process, the above model is a dynamic optimization problem with path dependence. The article proposed forward dynamic regularization method to solve. Finally, empirical studies are conducted to compare the changes of the optimal investment ratio and the final wealth of different entropy value portfolios, and the validity of the model and the algorithm are verified.