The Possibilistic Mean-Variance Model with Uncertain Possibility Distributions
The possibilistic mean–variance (MV) model is the counterpart of Markowitz’s MV model in the possibility theory. This study aims to examine the possibilistic MV model when the possibility distributions of stock returns are uncertain triangular fuzzy numbers. We define an uncertainty vector and use i...
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Mehmet Akif Ersoy University
2024-06-01
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| Series: | Mehmet Akif Ersoy Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/3530767 |
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| author | Furkan Göktaş |
| author_facet | Furkan Göktaş |
| author_sort | Furkan Göktaş |
| collection | DOAJ |
| description | The possibilistic mean–variance (MV) model is the counterpart of Markowitz’s MV model in the possibility theory. This study aims to examine the possibilistic MV model when the possibility distributions of stock returns are uncertain triangular fuzzy numbers. We define an uncertainty vector and use its ellipsoidal uncertainty set in a minimax optimization problem to model this uncertainty. We also show that this minimax optimization problem reduces to a strictly convex minimization problem. Thus, unlike the possibilistic MV model, we get diversified optimal portfolios uniquely with our approach. After laying down the theoretical points of our approach, we illustrate it with a real-world example in the literature by using a software package for convex optimization. To the best of our knowledge, this is the first paper that considers uncertain possibility distributions in the possibilistic MV model. |
| format | Article |
| id | doaj-art-96aefb6f9eb84398af401ed897aefe1b |
| institution | Kabale University |
| issn | 2149-1658 |
| language | English |
| publishDate | 2024-06-01 |
| publisher | Mehmet Akif Ersoy University |
| record_format | Article |
| series | Mehmet Akif Ersoy Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi |
| spelling | doaj-art-96aefb6f9eb84398af401ed897aefe1b2025-01-27T13:10:30ZengMehmet Akif Ersoy UniversityMehmet Akif Ersoy Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi2149-16582024-06-0111253555010.30798/makuiibf.1389261273The Possibilistic Mean-Variance Model with Uncertain Possibility DistributionsFurkan Göktaş0https://orcid.org/0000-0001-9291-3912Karabük ÜniversitesiThe possibilistic mean–variance (MV) model is the counterpart of Markowitz’s MV model in the possibility theory. This study aims to examine the possibilistic MV model when the possibility distributions of stock returns are uncertain triangular fuzzy numbers. We define an uncertainty vector and use its ellipsoidal uncertainty set in a minimax optimization problem to model this uncertainty. We also show that this minimax optimization problem reduces to a strictly convex minimization problem. Thus, unlike the possibilistic MV model, we get diversified optimal portfolios uniquely with our approach. After laying down the theoretical points of our approach, we illustrate it with a real-world example in the literature by using a software package for convex optimization. To the best of our knowledge, this is the first paper that considers uncertain possibility distributions in the possibilistic MV model.https://dergipark.org.tr/en/download/article-file/3530767convex optimizationfuzzy setnormal distributionportfolio selectionpossibility theorytriangular fuzzy number |
| spellingShingle | Furkan Göktaş The Possibilistic Mean-Variance Model with Uncertain Possibility Distributions Mehmet Akif Ersoy Üniversitesi İktisadi ve İdari Bilimler Fakültesi Dergisi convex optimization fuzzy set normal distribution portfolio selection possibility theory triangular fuzzy number |
| title | The Possibilistic Mean-Variance Model with Uncertain Possibility Distributions |
| title_full | The Possibilistic Mean-Variance Model with Uncertain Possibility Distributions |
| title_fullStr | The Possibilistic Mean-Variance Model with Uncertain Possibility Distributions |
| title_full_unstemmed | The Possibilistic Mean-Variance Model with Uncertain Possibility Distributions |
| title_short | The Possibilistic Mean-Variance Model with Uncertain Possibility Distributions |
| title_sort | possibilistic mean variance model with uncertain possibility distributions |
| topic | convex optimization fuzzy set normal distribution portfolio selection possibility theory triangular fuzzy number |
| url | https://dergipark.org.tr/en/download/article-file/3530767 |
| work_keys_str_mv | AT furkangoktas thepossibilisticmeanvariancemodelwithuncertainpossibilitydistributions AT furkangoktas possibilisticmeanvariancemodelwithuncertainpossibilitydistributions |