Mathematical Analyses of the Upper and Lower Possibilistic Mean – Variance Models and Their Extensions to Multiple Scenarios

Furkan Göktaş

doi:10.28979/jarnas.1216406

Araştırma Makalesi

Yıl 2023, Cilt: 9 Sayı: 2, 311 - 322, 30.06.2023

Furkan Göktaş

https://doi.org/10.28979/jarnas.1216406

Öz

Anahtar Kelimeler

Max-min optimization, portfolio selection, possibility theory, scenario analysis, trapezoidal fuzzy numbers

Destekleyen Kurum

Yok

Proje Numarası

Yok

Teşekkür

Yok

Kaynakça

Biswas, A., Verma, S., & Ojha, D. B. (2017). Optimality and convexity theorems for linear fractional programming problem. International Journal of Computational and Applied Mathematics, 12(3), 911-916. Retrieved from: https://www.ripublication.com/ijcam17/ijcamv12n3_27.pdf
Carlsson, C., Fullér, R., & Majlender, P. (2002). A possibilistic approach to selecting portfolios with highest utility score. Fuzzy Sets and Systems, 131(1), 13-21. DOI: https://doi.org/10.1016/S0165-0114(01)00251-2
Corazza, M., & Nardelli, C. (2019). Possibilistic mean–variance portfolios versus probabilistic ones: the winner is... Decisions in Economics and Finance, 42(1), 51-75. DOI: https://doi.org/10.1007/s10203-019-00234-1
Fullér, R., & Harmati, I. Á. (2018). On Possibilistic Dependencies: A Short Survey of Recent Developments. Soft Computing Based Optimization and Decision Models, 261-273. DOI: https://doi.org/10.1007/978-3-319-64286-4_16
Göktaş, F., & Duran, A. (2020). Olabilirlik ortalama–varyans modelinin matematiksel analizi. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 22(1), 80-91. DOI: https://doi.org/10.25092/baunfbed.677022 Klir, G. and Yuan, B. (1995). Fuzzy Sets and Fuzzy Logic. Prentice Hall.
Kosinski, W. (2006). On fuzzy number calculus. International Journal of Applied Mathematics and Computer Science, 16(1), 51-57. Retrieved from: http://matwbn.icm.edu.pl/ksiazki/amc/amc16/amc1614.pdf
Rustem, B., Becker, R. G., & Marty, W. (2000). Robust min–max portfolio strategies for rival forecast and risk scenarios. Journal of Economic Dynamics and Control, 24(11-12), 1591-1621. DOI: https://doi.org/10.1016/S0165-1889(99)00088-3
Tanaka, H., & Guo, P. (1999). Portfolio selection based on upper and lower exponential possibility distributions. European Journal of Operational Research, 114(1), 115-126. DOI: https://doi.org/10.1016/S0377-2217(98)00033-2
Tanaka, H., Guo, P., & Türksen, I. B. (2000). Portfolio selection based on fuzzy probabilities and possibility distributions. Fuzzy Sets and Systems, 111(3), 387-397. DOI: https://doi.org/10.1016/S0165-0114(98)00041-4
Taş, O., Kahraman, C., & Güran, C. B. (2016). A scenario based linear fuzzy approach in portfolio selection problem: application in the Istanbul Stock Exchange. Journal of Multiple-Valued Logic & Soft Computing, 26(3-5), 269-294. Retrieved from: http://www.oldcitypublishing.com/pdf/7431
Zhang, W. G. (2007). Possibilistic mean–standard deviation models to portfolio selection for bounded assets. Applied Mathematics and Computation, 189(2), 1614-1623. DOI: https://doi.org/10.1016/j.amc.2006.12.080
Zhang, W. G., Wang, Y. L., Chen, Z. P., & Nie, Z. K. (2007). Possibilistic mean-variance models and efficient frontiers for portfolio selection problem. Information Sciences, 177(13), 2787–2801. DOI: https://doi.org/10.1016/j.ins.2007.01.030
Zhang, W. G., Zhang, X. L., & Xiao, W. L. (2009). Portfolio selection under possibilistic mean–variance utility and a SMO algorithm. European Journal of Operational Research, 197(2), 693-700. DOI: https://doi.org/10.1016/j.ejor.2008.07.011
Zhang, Y., Li, X., & Guo, S. (2018). Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature. Fuzzy Optimization and Decision Making, 17(2), 125-158. DOI: https://doi.org/10.1007/s10700-017-9266-z
Zimmermann, H. J. (2001). Fuzzy Set Theory and Its Applications. Springer.

Mathematical Analyses of the Upper and Lower Possibilistic Mean – Variance Models and Their Extensions to Multiple Scenarios

Yıl 2023, Cilt: 9 Sayı: 2, 311 - 322, 30.06.2023

Furkan Göktaş

https://doi.org/10.28979/jarnas.1216406

Öz

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.

Anahtar Kelimeler

Max-min optimization, portfolio selection, possibility theory, scenario analysis, trapezoidal fuzzy numbers

Proje Numarası

Yok

Kaynakça

Biswas, A., Verma, S., & Ojha, D. B. (2017). Optimality and convexity theorems for linear fractional programming problem. International Journal of Computational and Applied Mathematics, 12(3), 911-916. Retrieved from: https://www.ripublication.com/ijcam17/ijcamv12n3_27.pdf
Carlsson, C., Fullér, R., & Majlender, P. (2002). A possibilistic approach to selecting portfolios with highest utility score. Fuzzy Sets and Systems, 131(1), 13-21. DOI: https://doi.org/10.1016/S0165-0114(01)00251-2
Corazza, M., & Nardelli, C. (2019). Possibilistic mean–variance portfolios versus probabilistic ones: the winner is... Decisions in Economics and Finance, 42(1), 51-75. DOI: https://doi.org/10.1007/s10203-019-00234-1
Fullér, R., & Harmati, I. Á. (2018). On Possibilistic Dependencies: A Short Survey of Recent Developments. Soft Computing Based Optimization and Decision Models, 261-273. DOI: https://doi.org/10.1007/978-3-319-64286-4_16
Göktaş, F., & Duran, A. (2020). Olabilirlik ortalama–varyans modelinin matematiksel analizi. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 22(1), 80-91. DOI: https://doi.org/10.25092/baunfbed.677022 Klir, G. and Yuan, B. (1995). Fuzzy Sets and Fuzzy Logic. Prentice Hall.
Kosinski, W. (2006). On fuzzy number calculus. International Journal of Applied Mathematics and Computer Science, 16(1), 51-57. Retrieved from: http://matwbn.icm.edu.pl/ksiazki/amc/amc16/amc1614.pdf
Rustem, B., Becker, R. G., & Marty, W. (2000). Robust min–max portfolio strategies for rival forecast and risk scenarios. Journal of Economic Dynamics and Control, 24(11-12), 1591-1621. DOI: https://doi.org/10.1016/S0165-1889(99)00088-3
Tanaka, H., & Guo, P. (1999). Portfolio selection based on upper and lower exponential possibility distributions. European Journal of Operational Research, 114(1), 115-126. DOI: https://doi.org/10.1016/S0377-2217(98)00033-2
Tanaka, H., Guo, P., & Türksen, I. B. (2000). Portfolio selection based on fuzzy probabilities and possibility distributions. Fuzzy Sets and Systems, 111(3), 387-397. DOI: https://doi.org/10.1016/S0165-0114(98)00041-4
Taş, O., Kahraman, C., & Güran, C. B. (2016). A scenario based linear fuzzy approach in portfolio selection problem: application in the Istanbul Stock Exchange. Journal of Multiple-Valued Logic & Soft Computing, 26(3-5), 269-294. Retrieved from: http://www.oldcitypublishing.com/pdf/7431
Zhang, W. G. (2007). Possibilistic mean–standard deviation models to portfolio selection for bounded assets. Applied Mathematics and Computation, 189(2), 1614-1623. DOI: https://doi.org/10.1016/j.amc.2006.12.080
Zhang, W. G., Wang, Y. L., Chen, Z. P., & Nie, Z. K. (2007). Possibilistic mean-variance models and efficient frontiers for portfolio selection problem. Information Sciences, 177(13), 2787–2801. DOI: https://doi.org/10.1016/j.ins.2007.01.030
Zhang, W. G., Zhang, X. L., & Xiao, W. L. (2009). Portfolio selection under possibilistic mean–variance utility and a SMO algorithm. European Journal of Operational Research, 197(2), 693-700. DOI: https://doi.org/10.1016/j.ejor.2008.07.011
Zhang, Y., Li, X., & Guo, S. (2018). Portfolio selection problems with Markowitz’s mean–variance framework: a review of literature. Fuzzy Optimization and Decision Making, 17(2), 125-158. DOI: https://doi.org/10.1007/s10700-017-9266-z
Zimmermann, H. J. (2001). Fuzzy Set Theory and Its Applications. Springer.

Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Mühendislik
Bölüm	Makaleler
Yazarlar	Furkan Göktaş 0000-0001-9291-3912
Proje Numarası	Yok
Erken Görünüm Tarihi	21 Haziran 2023
Yayımlanma Tarihi	30 Haziran 2023
Gönderilme Tarihi	8 Aralık 2022
Yayımlandığı Sayı	Yıl 2023 Cilt: 9 Sayı: 2

Kaynak Göster

APA	Göktaş, F. (2023). 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, 9(2), 311-322. https://doi.org/10.28979/jarnas.1216406
AMA	Göktaş F. Mathematical Analyses of the Upper and Lower Possibilistic Mean – Variance Models and Their Extensions to Multiple Scenarios. JARNAS. Haziran 2023;9(2):311-322. doi:10.28979/jarnas.1216406
Chicago	Göktaş, Furkan. “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 9, sy. 2 (Haziran 2023): 311-22. https://doi.org/10.28979/jarnas.1216406.
EndNote	Göktaş F (01 Haziran 2023) 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 9 2 311–322.
IEEE	F. Göktaş, “Mathematical Analyses of the Upper and Lower Possibilistic Mean – Variance Models and Their Extensions to Multiple Scenarios”, JARNAS, c. 9, sy. 2, ss. 311–322, 2023, doi: 10.28979/jarnas.1216406.
ISNAD	Göktaş, Furkan. “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 9/2 (Haziran 2023), 311-322. https://doi.org/10.28979/jarnas.1216406.
JAMA	Göktaş F. Mathematical Analyses of the Upper and Lower Possibilistic Mean – Variance Models and Their Extensions to Multiple Scenarios. JARNAS. 2023;9:311–322.
MLA	Göktaş, Furkan. “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, c. 9, sy. 2, 2023, ss. 311-22, doi:10.28979/jarnas.1216406.
Vancouver	Göktaş F. Mathematical Analyses of the Upper and Lower Possibilistic Mean – Variance Models and Their Extensions to Multiple Scenarios. JARNAS. 2023;9(2):311-22.