Uncertain random portfolio selection with different mental accounts based on mixed data

Due to the complexity of security markets, securities with massive effective data, invalid data and insufficient data may exist at the same time. When there are massive effective data, the security returns are regarded as random variables, or they can be regarded as uncertain variables when the data are insufficient or invalid. The common portfolio selection problem assumes that the investors put money into one mental account for management. Considering that the investors invest money in separate accounts in reality, this paper discusses a portfolio selection problem with different mental accounts under uncertain random environment. Firstly, we formulate an uncertain random model for the portfolio optimization problem with random risky securities and uncertain risky securities. The chance distributions of uncertain random variables are derived when the variables obey different distributions. On this basis, two equivalent forms of the uncertain random portfolio model based on mental accounts are presented. Finally, numerical simulations with two and three mental accounts are conducted to analyze the reality and practicability of the established models.