中文摘要：

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。

英文摘要：

In this paper,taking into account borrowing constraints,threshold constraints,transaction costs and risk control,we present a new multi-period possibilistic mean entropy portfolio selection model in which the return level is quantified by the possibilistic mean value of return,entropy is used as the measure of risk. The smaller the entropy value is, the less uncertainty the portfolio return contains, and thus, the safer the portfolio is. Furthermore, as a measure of risk, entropy is free from reliance on symmetrical distributions of security returns. Based on the theories of possibility, the proposed model is transformed into a crisp nonlinear dynamic optimization problem by using fuzzy programming approach. Because of the transaction costs,the proposed model is a nonlinearly dynamic optimization problem with path dependence. Furthermore,a forward dynamic programming method is designed to obtain the optimal portfolio strategy. Finally,the comparison analysis of the different terminal wealth is provided by an example to illustrate the efficiency of the proposed model and the designed algorithm.