Financial market is a complex system full of unknown and indeterminacy. It is well known that uncertainty and randomness are two basic types of indeterminacy. Hence, the complexity of real financial markets may lead to various types of security returns. They are usually assumed as random variables when there are enough historical data. If there is a lack of available data, they can be considered as uncertain variables. However, uncertainty and randomness often exist simultaneously. In this paper, we consider a portfolio optimization problem in real financial markets with both uncertainty and randomness. First, the skewnesses for three kinds of uncertain random variables are derived. Then, in an uncertain random environment, considering different risk preferences, a mean-variance-skewness model for the portfolio optimization problem is proposed. In addition, we use the normalization method to eliminate the impact of investment returns and risks of different units. Finally, numerical simulations are carried out to show that the proposed model is realistic and applicable.

金融市场是一个充满未知和不确定性的复杂系统。众所周知，不确定性和随机性是不确定性的两种基本类型。因此，真实金融市场的复杂性可能会导致各种类型的证券收益。当有足够的历史数据时，它们通常被假定为随机变量。如果缺乏可用数据，它们可以被视为不确定变量。然而，不确定性和随机性往往同时存在。在本文中，我们考虑具有不确定性和随机性的真实金融市场中的投资组合优化问题。首先，推导出三种不确定随机变量的偏度。然后，在不确定的随机环境下，考虑不同的风险偏好，提出了投资组合优化问题的均值-方差-偏度模型。此外，我们采用归一化的方法来消除不同单位的投资收益和风险的影响。最后,通过数值模拟验证了所提出的模型的真实性和适用性。