Experton approach to vague information in portfolio selection problem with many views

Abstract

This paper presents many expert fuzzy extensions of the Black-Litterman portfolio selection model. Black and Litterman identified two sources of information regarding the expected returns, and they combined these two sources of information in one expected return formula. The first source of information is the expected returns from the Capital Asset Pricing Model and thus should hold if the market is in equilibrium. The second source of information is the views held by the investors. The presented extension, owing to the use of a fuzzy random variable and experton, includes two elements that are important from a practical perspective: linguistic information and the multiple experts' views. This paper introduces the model extension sequentially and then illustrates it by empirical example.