Multi-objective portfolio selection problem using admissible order vector space

Abstract

In this paper, multiobjective optimization problem is considered in which parameters of objective functions (expected return, risk, skewness, kurtosis, and entropy) are estimated as a closed interval. A solution methodology has been developed to find an efficient portfolio using the bijective representation of an interval and admissible-order relation scenario. For this, the concept of admissible order on the set of intervals is firstly extended. Secondly, the proposed model is transformed into an interval weighted sum scalarization multi-objective optimization problem using an admissible order and interval ordered weighted aggregation operator. The transformed model's solution can be obtained by solving many deterministic programming problems, which will provide an efficient investment policy to the proposed model. Further, the proposed technique is illustrated in an empirical example using the historical data taken from the Indian stock market to show the results’ applicability.