Efficient solutions for vector optimization problem on an extended interval vector space and its application to portfolio optimization

Abstract

In this paper, a generalized interval vector space is investigated and defined as an ordered relation in the form of a bijective linear transformation of its onto a real vector space. The ordered relation is utilized to formulate an interval optimization problem in the same manner as a classical multi-objective programming problem. A methodology that addresses the existence of efficient solutions for the multi-objective interval optimization problem has also been discussed. Various numerical examples are described to illustrate and substantiate all developed concepts. Furthermore, the multi-objective portfolio rebalancing problem for a time horizon is designed based on the developed interval vector optimization. An algorithm using exhaustive solution technology has been proposed to achieve an efficient investment strategy. Finally, its applicability and efficacy are analyzed using Bombay Stock Exchange India data sets.