Mathematical Analyses of the Upper and Lower Possibilistic Mean – Variance Models and Their Extensions to Multiple Scenarios
Possibility theory is the one of the most important and widely used uncertainty theories because it is closely related to the imprecise probability and expert knowledge. The possibilistic mean - variance (MV) model is the counterpart of the Markowitz’s MV model in the possibility theory. There are v...
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Çanakkale Onsekiz Mart University
2023-06-01
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| Series: | Journal of Advanced Research in Natural and Applied Sciences |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/2820383 |
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| author | Furkan Göktaş |
| author_facet | Furkan Göktaş |
| author_sort | Furkan Göktaş |
| collection | DOAJ |
| description | Possibility theory is the one of the most important and widely used uncertainty theories because it is closely related to the imprecise probability and expert knowledge. The possibilistic mean - variance (MV) model is the counterpart of the Markowitz’s MV model in the possibility theory. There are variants of the possibilistic MV model, which are called as the upper and lower possibilistic MV models. However, to the best of our knowledge, analytical solutions and exact efficient frontiers of these variants are not presented in the literature when the possibil-ity distributions are given with trapezoidal fuzzy numbers. In this study, under this assumption, we make mathemat-ical analyses of the upper and lower possibilistic MV models and derive their analytical solutions and exact efficient frontiers. Based on the max-min optimization framework, we also propose their extensions where there are multiple upper (lower) possibilistic mean scenarios. We show that the proposed extensions have the ease of use as the upper and lower possibilistic MV models. We also illustrate and compare the upper and lower possibilistic mean - variance models and their proposed extensions with an explanatory example. As we expect, we see that these extensions can be effectively used in portfolio selection by conservative investors. |
| format | Article |
| id | doaj-art-0daa00e63ef548beb379a9604b86282c |
| institution | Kabale University |
| issn | 2757-5195 |
| language | English |
| publishDate | 2023-06-01 |
| publisher | Çanakkale Onsekiz Mart University |
| record_format | Article |
| series | Journal of Advanced Research in Natural and Applied Sciences |
| spelling | doaj-art-0daa00e63ef548beb379a9604b86282c2025-02-05T17:57:35ZengÇanakkale Onsekiz Mart UniversityJournal of Advanced Research in Natural and Applied Sciences2757-51952023-06-019231132210.28979/jarnas.1216406453Mathematical Analyses of the Upper and Lower Possibilistic Mean – Variance Models and Their Extensions to Multiple ScenariosFurkan Göktaş0https://orcid.org/0000-0001-9291-3912KARABÜK ÜNİVERSİTESİPossibility theory is the one of the most important and widely used uncertainty theories because it is closely related to the imprecise probability and expert knowledge. The possibilistic mean - variance (MV) model is the counterpart of the Markowitz’s MV model in the possibility theory. There are variants of the possibilistic MV model, which are called as the upper and lower possibilistic MV models. However, to the best of our knowledge, analytical solutions and exact efficient frontiers of these variants are not presented in the literature when the possibil-ity distributions are given with trapezoidal fuzzy numbers. In this study, under this assumption, we make mathemat-ical analyses of the upper and lower possibilistic MV models and derive their analytical solutions and exact efficient frontiers. Based on the max-min optimization framework, we also propose their extensions where there are multiple upper (lower) possibilistic mean scenarios. We show that the proposed extensions have the ease of use as the upper and lower possibilistic MV models. We also illustrate and compare the upper and lower possibilistic mean - variance models and their proposed extensions with an explanatory example. As we expect, we see that these extensions can be effectively used in portfolio selection by conservative investors.https://dergipark.org.tr/en/download/article-file/2820383max-min optimizationportfolio selectionpossibility theoryscenario analysistrapezoidal fuzzy numbersmax-min optimizationportfolio selectionpossibility theoryscenario analysistrapezoidal fuzzy numbers |
| spellingShingle | Furkan Göktaş Mathematical Analyses of the Upper and Lower Possibilistic Mean – Variance Models and Their Extensions to Multiple Scenarios Journal of Advanced Research in Natural and Applied Sciences max-min optimization portfolio selection possibility theory scenario analysis trapezoidal fuzzy numbers max-min optimization portfolio selection possibility theory scenario analysis trapezoidal fuzzy numbers |
| title | Mathematical Analyses of the Upper and Lower Possibilistic Mean – Variance Models and Their Extensions to Multiple Scenarios |
| title_full | Mathematical Analyses of the Upper and Lower Possibilistic Mean – Variance Models and Their Extensions to Multiple Scenarios |
| title_fullStr | Mathematical Analyses of the Upper and Lower Possibilistic Mean – Variance Models and Their Extensions to Multiple Scenarios |
| title_full_unstemmed | Mathematical Analyses of the Upper and Lower Possibilistic Mean – Variance Models and Their Extensions to Multiple Scenarios |
| title_short | Mathematical Analyses of the Upper and Lower Possibilistic Mean – Variance Models and Their Extensions to Multiple Scenarios |
| title_sort | mathematical analyses of the upper and lower possibilistic mean variance models and their extensions to multiple scenarios |
| topic | max-min optimization portfolio selection possibility theory scenario analysis trapezoidal fuzzy numbers max-min optimization portfolio selection possibility theory scenario analysis trapezoidal fuzzy numbers |
| url | https://dergipark.org.tr/en/download/article-file/2820383 |
| work_keys_str_mv | AT furkangoktas mathematicalanalysesoftheupperandlowerpossibilisticmeanvariancemodelsandtheirextensionstomultiplescenarios |