The outbreak of uncertain events, e.g., financial crisis, regional conflict and abrupt contagion, has a significant impact on residents’ income. Hence, the wealth management and portfolio selection become more and more important. In addition, the behavioral finance believes that decision-making process of the investors not only depend on utility maximization, but also on who to compare with. It differs from the traditional finance based on rational cognitive acquiring and decision-making of agents, in this paper, we consider both investment uncertainty and investment utility with reference level for portfolio selection. First, we introduce the uncertainty theory and loss aversion utility with reference level based on behavioral finance. Then we study an uncertain multi-period portfolio selection problem. Moreover, we formulate an uncertain behavioral portfolio selection model with three objective functions for which we propose an equivalent program consisting of a main model and two auxiliary models for tri-objective optimization model. Thereafter, we use a modified evolutionary root system growth algorithm to solve the transformed models. Finally, a numerical simulation allows to show the practicability of proposed models and validity of modified algorithm.

中文翻译：

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使用改进的进化根系统增长算法，基于不确定性理论的具有损失厌恶和参考水平的三目标行为投资组合选择模型

金融危机、地区冲突、突发疫情等不确定事件的爆发，对居民收入产生重大影响。因此，财富管理和投资组合选择变得越来越重要。此外，行为金融学认为，投资者的决策过程不仅取决于效用最大化，还取决于与谁进行比较。与基于代理人理性认知获取和决策的传统金融不同，本文同时考虑投资不确定性和投资效用，为投资组合选择提供参考水平。首先，我们介绍了基于行为金融学的不确定性理论和具有参考水平的损失厌恶效用。然后我们研究一个不确定的多时期投资组合选择问题。此外，我们制定了具有三个目标函数的不确定行为投资组合选择模型，为此我们提出了一个由一个主模型和两个辅助模型组成的三目标优化模型的等效程序。此后，我们使用改进的进化根系统生长算法来求解转换后的模型。最后，数值模拟可以显示所提出模型的实用性和修改算法的有效性。