Intuitionistic fuzzy optimistic and pessimistic multi-period portfolio optimization models

Abstract

There are myriad works that deal with the fuzzy multi-period portfolio selection problem, but when we talk about multi-period portfolio selection in an intuitionistic fuzzy realm, to the best of our knowledge, there is no research work that deals with the same. So, to fill this research gap, we propose an intuitionistic fuzzy multi-period portfolio selection model with the objectives of maximization of the terminal wealth and minimization of the cumulative risk subject to several realistic constraints such as complete capital utilization, no short selling, fixed transaction costs for buying and selling, bounds on the desired returns of each period, cardinality constraint, and bounds on the minimal and the maximal proportion of the capital allocated to an asset. The membership and non-membership of the objectives are modeled using their extreme values. The proposed approach provides avenues for the inclusion and minimization of the hesitation degree into decision making, thereby resulting in a significantly better portfolio. Parameters $\theta _W$ and $\theta _{Va}$ are used to introduce the hesitation in the model, and, based on their values, the model is further categorized into optimistic and pessimistic intuitionistic fuzzy multi-period portfolio selection models for optimistic and pessimistic investors, respectively. The max–min approach is used to solve the proposed models. Furthermore, a numerical illustration is presented to exhibit the virtues of the proposed model.