Cross-entropy based multi-objective uncertain portfolio selection problem

Abstract

In most real life investment situations future security returns are represented mainly based on expert’s judgments due to the occurrence of unexpected incidents in economic and social changes or lack of historical data. In order to tackle such uncertainties, the returns of the securities are evaluated by the experts instead of historical data. In this study, a multi-objective uncertain portfolio selection model has been proposed by defining average return as expected value, risk as variance and divergence among security returns as cross-entropy where the security returns are considered as uncertain variables. The transformed deterministic form of the proposed model is presented by considering security returns as linear uncertain variables. The deterministic model is then solved by using two multi-objective genetic algorithms (MOGAs), namely, Nondominated Sorting Genetic Algorithm II (NSGA-II) and Archive-Based hYbrid Scatter Search (AbYSS). We use a dataset from the Shenzhen Stock Exchange to illustrate the performance of the algorithms. Finally, a comparative study is performed in terms of certain performance matrices among NSGA-II and AbYSS.