Portfolio Model Based On Fuzzy Interval Minimax Rules

Markowitz portfolio theory can be considered as the portfolio theory with M-V rules. Recently, many researchers pay more attention to portfolio problems based on Minimax rule. In the paper, we discuss the portfolio model based on Minimax rule with fuzzy interval. Because markets have a variety of uncertain, the precise value of the expected return of securities is undetermined. As a special kind of fuzzy numbers, interval number is a powerful tool to deal with the uncertainty problem. Therefore, it is a significant problem to research portfolio model based on Minimax rule with fuzzy interval.First, we assume that the return of securities is expressed as a variable over an interval, not a definite value. We consider the absolute deviation between securities return and expected return as risk measure, then construct the portfolio model based on Minimax rule with fuzzy interval.Secondly, we introduce order relation, and transform fuzzy interval model into a clear number model, then get the interval solution of the model. By comparing the optimal solution in this paper with that of the model without fuzzy interval, we can derive that the solution to the model in the setting of fuzzy is much better.Finally, the model posed in this paper was extended to the model with transaction costs. By a similar argument, we can get the interval solution. This model can be regarded as a natural generalization of ordinarily portfolio model under the Minimax rule.