Black-Litterman model with intuitionistic fuzzy posterior return

TL;DR

This paper introduces a novel variant of the Black-Litterman model that incorporates intuitionistic fuzzy numbers to better handle uncertainty in expert views and prior returns, with proofs of the existence of posterior returns.

Contribution

It extends the Black-Litterman model by modeling expert views as intuitionistic fuzzy numbers, addressing Knightian uncertainty in a new way.

Findings

Posterior return exists under the proposed model.

Posterior return is an intuitionistic fuzzy probabilistic set.

The model effectively captures uncertainty in expert opinions.

Abstract

The main objective is to present a some variant of the Black - Litterman model. We consider the canonical case when priori return is determined by means such excess return from the CAPM market portfolio which is derived using reverse optimization method. Then the a priori return is at risk quantified uncertainty. On the side, intensive discussion shows that the experts' views are under knightian uncertainty. For this reason, we propose such variant of the Black - Litterman model in which the experts' views are described as intuitionistic fuzzy number. The existence of posterior return is proved for this case.We show that then posterior return is an intuitionistic fuzzy probabilistic set.