This paper discusses an uncertain multi-period portfolio selection problem in the situation where the future security return rates are given by experts’ estimations instead of historical data. In financial market, investors may have different attitudes towards risk for different goals. In order to reflect these conflicting risk attitudes for different goals, mental accounts are introduced to the investment. In addition, investment strategies may be affected by some realistic constraints such as background risk, liquidity risk, transaction cost and cardinality constraint. Based on uncertainty theory, a nonlinear multi-period portfolio selection model is proposed with consideration of mental accounts and realistic constraints. In the model, indeterminate quantities such as security return rates and turnover rates are assumed to be uncertain variables. Within the framework of uncertainty theory, we discuss the equivalents of the model and show that the nonlinear model can be equivalently transformed into a linear programming model. Finally, a case study is given to illustrate the performance of the proposed model.

本文讨论了一种不确定的多期投资组合选择问题，这种情况下，未来的安全收益率是由专家的估计而不是历史数据给出的。在金融市场中，投资者对于不同目标的风险可能有不同的态度。为了反映这些针对不同目标的相互矛盾的风险态度，将心理账户引入了该投资。此外，投资策略可能会受到一些实际约束的影响，例如背景风险，流动性风险，交易成本和基数约束。基于不确定性理论，提出了一种考虑心理因素和现实约束的非线性多时期投资组合选择模型。在模型中 不确定数量（例如安全退货率和周转率）是不确定的变量。在不确定性理论的框架内，我们讨论了模型的等效项，并表明非线性模型可以等效地转换为线性规划模型。最后，通过案例研究来说明所提出模型的性能。