Uncertain events frequently occur in today’s financial markets. Consequently, the issue of portfolio selection is becoming increasingly significant. This paper thoroughly considers the complexities of stock returns in real-world scenarios and employs uncertain differential equations (UDE), uncertain time series analysis (UTSA), stochastic differential equations (SDE), and random time series analysis (RTSA) to predict stock returns, thereby enhancing the accuracy of these predictions. Furthermore, this paper addresses investors’ preferences and the limitations of using variance as a measure of investment risk. It introduces a risk preference factor and proposes an uncertain random mean-lower variance model. Finally, a genetic algorithm is utilized to solve the model, and numerical simulations are conducted to demonstrate the model’s practicality.

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