A risk index model for portfolio selection with returns subject to experts' estimations

Portfolio selection is concerned with selecting an optimal portfolio that can strike a balance between maximizing the return and minimizing the risk among a large number of securities. Traditionally, security returns were regarded as random variables. However, there are cases that the predictions of security returns are given mainly based on experts' judgements and estimations rather than historical data. In this paper, we introduce a new type of variable to reflect the subjective estimations of the security returns. A risk index for uncertain portfolio selection is proposed and a new safe criterion for judging the portfolio investment is introduced. Based on the proposed risk index, a new mean-risk index model is developed and its crisp forms are given. In addition, to illustrate the application of the model, two numerical examples are also presented.