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

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Published in:	Proceedings of the National Academy of Sciences, India, Section A, physical sciences Vol. 95; no. 1; pp. 55 - 70
Main Authors:	Chhatri, Sanjoy, Bhattacharya, Debasish
Format:	Journal Article
Language:	English
Published:	New Delhi Springer India 01.03.2025
Subjects:	Applied and Technical Physics Atomic Molecular Optical and Plasma Physics Physics Physics and Astronomy Quantum Physics Research Article Portfolio optimization Uncertain variable Multi-objective programming 74PXX Efficient solution 90-XX
ISSN:	0369-8203, 2250-1762
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Abstract	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.
AbstractList	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.
Author	Bhattacharya, Debasish Chhatri, Sanjoy
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Subtitle	A New Mean-Variance-Skewness Model for Portfolio Optimization Using Three-Part Zigzag Uncertain Variable
Title	A New Mean-Variance-Skewness Model for Portfolio Optimization Using Three-Part Zigzag Uncertain Variable
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