Portfolio Selection Subject to Vague Experts' Judgments

This paper is written with two purposes in mind. First, it brings together some recent results in the area of mean-variance theory model validation for fuzzy systems in the existence of subjective measures suggested by experts. The central idea of the methods presented here is to map random uncertainty given a portfolio-selection model into fuzzy random uncertainty description, which is useful from an application and analysis point of view. The main contributions of the paper are (i) to explore the implications of fuzzy return indeterminacy on mean-variance optimal portfolio choice and (ii) to use bid-ask spread as a proxy measure of the indeterminacy or fuzzy nature of random returns. Second, this paper also presents a brief self-contained glimpse of empirical representations to practitioners unfamiliar with the field of fuzzy modeling. It is hoped that expositions such as this one will open new collaborations between other branches of fuzzy mathematics and asset-pricing theories