Mean-risk model for uncertain portfolio selection

This paper discusses the uncertain portfolio selection problem when security returns cannot be well reflected by historical data. It is proposed that uncertain variable should be used to reflect the experts’ subjective estimation of security returns. Regarding the security returns as uncertain variables, the paper introduces a risk curve and develops a mean-risk model. In addition, the crisp form of the model is provided. The presented numerical examples illustrate the application of the mean-risk model and show the disaster result of mistreating uncertain returns as random returns.