Multiobjective portfolio optimization using coherent fuzzy numbers in a credibilistic environment

In this paper, we propose a new credibility function for a fuzzy variable that can accommodate the attitude of the investor (pessimistic, optimistic, or neutral) along with capturing the return expectations. We use an adaptive index, which the investors can use to specify their general perception of the financial market. We extend the classic mean-variance model so that it provides greater flexibility to the investors in specifying their requirements viz., level of diversification, minimum and maximum level of investment in a particular asset, and the skewness requirement. We also replace variance with mean-absolute semideviation as a measure of quantifying risk, which is more realistic, and solve the resultant multiobjective credibility model with a real-coded genetic algorithm. Numerical examples have been provided at the end to illustrate the methodology and advantages of the model.