A New Mean-Variance-Skewness Model for Portfolio Optimization Using Three-Part Zigzag Uncertain Variable

A multi-objective portfolio selection problem involving newly introduced stocks has been studied here, and an innovative solution procedure for the same with a numerical illustration is also provided. The returns of these stocks are represented by a new uncertainty distribution, called the three-part zigzag uncertainty distribution, introduced in this paper. This newly defined uncertainty distribution function is regular and closer to an S-shaped curve than linear and zigzag uncertainty distribution functions. The properties of the three-part zigzag uncertainty distribution are studied, and the expression for the general order central moment of the distribution has been obtained. Using the expected value and the second, third order central moments, two maximizing objectives and one minimizing objective for the said optimization purpose are formed. Finally, using the “fmincon” function in Matlab 2018a, the constructed problem is solved. The solution obtained has been interpreted. The fact that it yields an efficient or Pareto optimal solution has also been proven.

Significance Statement A three-objective portfolio selection problem in an uncertain situation has been constructed using a newly defined uncertainty distribution. An innovative solution procedure that elicits efficient solutions is suggested to solve the problem. The work done can be applied to solve real-life portfolio selection problems with better accuracy.