Multi-criteria Credibilistic Portfolio Selection Model with Various Risk Comparisons Using Trapezoidal Fuzzy Variable

Jagdish Kumar Pahade; Manoj Jha

doi:doi:10.11648/j.acm.20211001.11

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Multi-criteria Credibilistic Portfolio Selection Model with Various Risk Comparisons Using Trapezoidal Fuzzy Variable

Jagdish Kumar Pahade, Manoj Jha

Published in Applied and Computational Mathematics (Volume 10, Issue 1)

Received: 12 January 2021 Accepted: 19 January 2021 Published: 10 February 2021

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Abstract

Dealing with problems on portfolio selection models fuzzy set theory is effectively interpolating investor’s attitude. The credibility theory (Branch of fuzzy set theory) is broadly utilized to describe uncertainty of the financial markets. We regard the return rate of each risky stock as a trapezoidal fuzzy number. Variance and semi-variance of fuzzy return on stocks are widely accepted as risk measures in portfolio selection models. This paper obtains credibilistic semi-variance of trapezoidal fuzzy variable and applied this concept to quantify the risk in stock fuzzy portfolio selection. A multi-criteria credibilistic mean-semivariance-skewness model is proposed with numerical illustration taking historical data set from the premier market for financial assets. Three objectives are taken into account namely, expected portfolio return, risk on expected portfolio return and portfolio skewness to construct multi-objective programming problem, along with cardinality constraint, complete capital utilization, floor and ceiling constraint, no short selling constraints. To solve the proposed multi-objective optimization problem, optimal goal programming approach is suggested. Finally, a case study is conducted to highlight the effectiveness of the proposed models through the real-world data from the Bombay Stock Exchange (BSE), an Indian premier market for financial stocks. Furthermore, results comparison of semi-variance as risk measure with other existing risk measures is performed.

Published in	Applied and Computational Mathematics (Volume 10, Issue 1)
DOI	10.11648/j.acm.20211001.11
Page(s)	1-9
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Trapezoidal Fuzzy Variables, Credibilistic Semi-variance, Fuzzy Portfolio Selection, Optimal Goal Programming

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Jagdish Kumar Pahade, Manoj Jha. (2021). Multi-criteria Credibilistic Portfolio Selection Model with Various Risk Comparisons Using Trapezoidal Fuzzy Variable. Applied and Computational Mathematics, 10(1), 1-9. https://doi.org/10.11648/j.acm.20211001.11

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Jagdish Kumar Pahade; Manoj Jha. Multi-criteria Credibilistic Portfolio Selection Model with Various Risk Comparisons Using Trapezoidal Fuzzy Variable. Appl. Comput. Math. 2021, 10(1), 1-9. doi: 10.11648/j.acm.20211001.11

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AMA Style

Jagdish Kumar Pahade, Manoj Jha. Multi-criteria Credibilistic Portfolio Selection Model with Various Risk Comparisons Using Trapezoidal Fuzzy Variable. Appl Comput Math. 2021;10(1):1-9. doi: 10.11648/j.acm.20211001.11

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@article{10.11648/j.acm.20211001.11,
  author = {Jagdish Kumar Pahade and Manoj Jha},
  title = {Multi-criteria Credibilistic Portfolio Selection Model with Various Risk Comparisons Using Trapezoidal Fuzzy Variable},
  journal = {Applied and Computational Mathematics},
  volume = {10},
  number = {1},
  pages = {1-9},
  doi = {10.11648/j.acm.20211001.11},
  url = {https://doi.org/10.11648/j.acm.20211001.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20211001.11},
  abstract = {Dealing with problems on portfolio selection models fuzzy set theory is effectively interpolating investor’s attitude. The credibility theory (Branch of fuzzy set theory) is broadly utilized to describe uncertainty of the financial markets. We regard the return rate of each risky stock as a trapezoidal fuzzy number. Variance and semi-variance of fuzzy return on stocks are widely accepted as risk measures in portfolio selection models. This paper obtains credibilistic semi-variance of trapezoidal fuzzy variable and applied this concept to quantify the risk in stock fuzzy portfolio selection. A multi-criteria credibilistic mean-semivariance-skewness model is proposed with numerical illustration taking historical data set from the premier market for financial assets. Three objectives are taken into account namely, expected portfolio return, risk on expected portfolio return and portfolio skewness to construct multi-objective programming problem, along with cardinality constraint, complete capital utilization, floor and ceiling constraint, no short selling constraints. To solve the proposed multi-objective optimization problem, optimal goal programming approach is suggested. Finally, a case study is conducted to highlight the effectiveness of the proposed models through the real-world data from the Bombay Stock Exchange (BSE), an Indian premier market for financial stocks. Furthermore, results comparison of semi-variance as risk measure with other existing risk measures is performed.},
 year = {2021}
}

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TY  - JOUR
T1  - Multi-criteria Credibilistic Portfolio Selection Model with Various Risk Comparisons Using Trapezoidal Fuzzy Variable
AU  - Jagdish Kumar Pahade
AU  - Manoj Jha
Y1  - 2021/02/10
PY  - 2021
N1  - https://doi.org/10.11648/j.acm.20211001.11
DO  - 10.11648/j.acm.20211001.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 1
EP  - 9
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20211001.11
AB  - Dealing with problems on portfolio selection models fuzzy set theory is effectively interpolating investor’s attitude. The credibility theory (Branch of fuzzy set theory) is broadly utilized to describe uncertainty of the financial markets. We regard the return rate of each risky stock as a trapezoidal fuzzy number. Variance and semi-variance of fuzzy return on stocks are widely accepted as risk measures in portfolio selection models. This paper obtains credibilistic semi-variance of trapezoidal fuzzy variable and applied this concept to quantify the risk in stock fuzzy portfolio selection. A multi-criteria credibilistic mean-semivariance-skewness model is proposed with numerical illustration taking historical data set from the premier market for financial assets. Three objectives are taken into account namely, expected portfolio return, risk on expected portfolio return and portfolio skewness to construct multi-objective programming problem, along with cardinality constraint, complete capital utilization, floor and ceiling constraint, no short selling constraints. To solve the proposed multi-objective optimization problem, optimal goal programming approach is suggested. Finally, a case study is conducted to highlight the effectiveness of the proposed models through the real-world data from the Bombay Stock Exchange (BSE), an Indian premier market for financial stocks. Furthermore, results comparison of semi-variance as risk measure with other existing risk measures is performed.
VL  - 10
IS  - 1
ER  -

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Author Information

Jagdish Kumar Pahade

Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal, India
Manoj Jha

Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal, India

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Jagdish Kumar Pahade, Manoj Jha. (2021). Multi-criteria Credibilistic Portfolio Selection Model with Various Risk Comparisons Using Trapezoidal Fuzzy Variable. Applied and Computational Mathematics, 10(1), 1-9. https://doi.org/10.11648/j.acm.20211001.11

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ACS Style

Jagdish Kumar Pahade; Manoj Jha. Multi-criteria Credibilistic Portfolio Selection Model with Various Risk Comparisons Using Trapezoidal Fuzzy Variable. Appl. Comput. Math. 2021, 10(1), 1-9. doi: 10.11648/j.acm.20211001.11

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AMA Style

Jagdish Kumar Pahade, Manoj Jha. Multi-criteria Credibilistic Portfolio Selection Model with Various Risk Comparisons Using Trapezoidal Fuzzy Variable. Appl Comput Math. 2021;10(1):1-9. doi: 10.11648/j.acm.20211001.11

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@article{10.11648/j.acm.20211001.11,
  author = {Jagdish Kumar Pahade and Manoj Jha},
  title = {Multi-criteria Credibilistic Portfolio Selection Model with Various Risk Comparisons Using Trapezoidal Fuzzy Variable},
  journal = {Applied and Computational Mathematics},
  volume = {10},
  number = {1},
  pages = {1-9},
  doi = {10.11648/j.acm.20211001.11},
  url = {https://doi.org/10.11648/j.acm.20211001.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20211001.11},
  abstract = {Dealing with problems on portfolio selection models fuzzy set theory is effectively interpolating investor’s attitude. The credibility theory (Branch of fuzzy set theory) is broadly utilized to describe uncertainty of the financial markets. We regard the return rate of each risky stock as a trapezoidal fuzzy number. Variance and semi-variance of fuzzy return on stocks are widely accepted as risk measures in portfolio selection models. This paper obtains credibilistic semi-variance of trapezoidal fuzzy variable and applied this concept to quantify the risk in stock fuzzy portfolio selection. A multi-criteria credibilistic mean-semivariance-skewness model is proposed with numerical illustration taking historical data set from the premier market for financial assets. Three objectives are taken into account namely, expected portfolio return, risk on expected portfolio return and portfolio skewness to construct multi-objective programming problem, along with cardinality constraint, complete capital utilization, floor and ceiling constraint, no short selling constraints. To solve the proposed multi-objective optimization problem, optimal goal programming approach is suggested. Finally, a case study is conducted to highlight the effectiveness of the proposed models through the real-world data from the Bombay Stock Exchange (BSE), an Indian premier market for financial stocks. Furthermore, results comparison of semi-variance as risk measure with other existing risk measures is performed.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Multi-criteria Credibilistic Portfolio Selection Model with Various Risk Comparisons Using Trapezoidal Fuzzy Variable
AU  - Jagdish Kumar Pahade
AU  - Manoj Jha
Y1  - 2021/02/10
PY  - 2021
N1  - https://doi.org/10.11648/j.acm.20211001.11
DO  - 10.11648/j.acm.20211001.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 1
EP  - 9
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20211001.11
AB  - Dealing with problems on portfolio selection models fuzzy set theory is effectively interpolating investor’s attitude. The credibility theory (Branch of fuzzy set theory) is broadly utilized to describe uncertainty of the financial markets. We regard the return rate of each risky stock as a trapezoidal fuzzy number. Variance and semi-variance of fuzzy return on stocks are widely accepted as risk measures in portfolio selection models. This paper obtains credibilistic semi-variance of trapezoidal fuzzy variable and applied this concept to quantify the risk in stock fuzzy portfolio selection. A multi-criteria credibilistic mean-semivariance-skewness model is proposed with numerical illustration taking historical data set from the premier market for financial assets. Three objectives are taken into account namely, expected portfolio return, risk on expected portfolio return and portfolio skewness to construct multi-objective programming problem, along with cardinality constraint, complete capital utilization, floor and ceiling constraint, no short selling constraints. To solve the proposed multi-objective optimization problem, optimal goal programming approach is suggested. Finally, a case study is conducted to highlight the effectiveness of the proposed models through the real-world data from the Bombay Stock Exchange (BSE), an Indian premier market for financial stocks. Furthermore, results comparison of semi-variance as risk measure with other existing risk measures is performed.
VL  - 10
IS  - 1
ER  -

Copy | Download