In the face of complex financial phenomena, describing the high uncertainties in financial markets remains a challenging issue in modelling and decision making. In this paper, chance theory is used to analyse the hybrid uncertainty that combines random returns and uncertain returns. We regard the total return as an uncertain random variable and study the uncertain random portfolio optimization problem. We first define the skewness of an uncertain random variable and derive some important properties and explicit expressions with deterministic distributions. These theoretical results help transform the model into a deterministic form. Then, uncertain random mean–variance–skewness portfolio optimization models and their corresponding equivalents are established to meet the diverse needs of investors. Finally, we provide two numerical experiments to illustrate the applicability of the proposed model, one of which demonstrates that the model can be applied in the area of energy finance. It is shown that when uncertain asset returns are asymmetric, this model can be used to make investment decisions for investors. We also find that a higher return is accompanied by higher risk and higher skewness.

面对复杂的金融现象，描述金融市场的高度不确定性仍然是建模和决策中的一个具有挑战性的问题。本文利用机会理论分析了随机收益与不确定收益相结合的混合不确定性。我们将总收益看成一个不确定随机变量，研究不确定随机投资组合优化问题。我们首先定义一个不确定随机变量的偏度，并推导出一些重要的性质和具有确定性分布的显式表达式。这些理论结果有助于将模型转化为确定性形式。然后，建立了不确定随机均值-方差-偏度组合优化模型及其对应的等价物，以满足投资者的多样化需求。最后，我们提供了两个数值实验来说明所提出模型的适用性，其中一个表明该模型可以应用于能源金融领域。结果表明，当不确定资产收益不对称时，该模型可用于投资者进行投资决策。我们还发现，更高的回报伴随着更高的风险和更高的偏度。