Ortogonal Olabilirlik Ortalama - Varyans Modeli

Year 2023, Volume: 6 Issue: Ek Sayı, 29 - 41, 20.12.2023

Furkan Göktaş

https://doi.org/10.47495/okufbed.1217550

Abstract

Olabilirlik teorisi, portföy seçimi probleminde en çok kullanılan araçlardan biridir. Çünkü kesin olmayan olasılığın modellenmesine ve uzman bilgisinin portföy seçimi problemine entegre edilmesine imkan verir. Ama olabilirlik ortalama - varyans (OV) modelinin ve bunun uzantılarının bazı sorunları vardır. Bu nedenle bu çalışmada kesin konveks kuadratik minimizasyona dayanan ortogonal olabilirlik OV modeli önerilmiştir. Ayrıca olabilirlik dağılımları üçgensel bulanık sayılar ile verildiğinde olabilirlik çarpıklığı tanımlanmıştır. Olabilirlik çarpıklığı önerilen modele kısıt olarak eklenebilir. Bu modelin analitik çözümü belirli şartlar altında elde edilmiştir. Ayrıca bu model açıklayıcı bir örnek ile tanıtılmıştır ve bu modelin sonuçları Olabilirlik OV modelinin sonuçları ile karşılaştırılmıştır.

Keywords

Portföy seçimi, Olabilirlik teorisi, Üçgensel bulanık sayılar, Konveks kuadratik minimizasyon, Uzman bilgisi, Olabilirlik çarpıklığı

Supporting Institution

Yok

Project Number

Yok

Thanks

Yok

Orthogonal Possibilistic Mean - Variance Model

Abstract

The possibility theory is one of the most used tools in portfolio selection problem. Because, it enables to model imprecise probability and integrate expert knowledge into portfolio selection problem. However, there are some problems in the possibilistic mean - variance (MV) model and its extensions. Therefore, in this study, we propose an orthogonal possibilistic MV model based on strictly convex quadratic minimization. We also define possibilistic skewness when possibility distributions are given with triangular fuzzy numbers. The possibilistic skewness can be added to the proposed model as a constraint. We derive its analytical solution under certain conditions. We also illustrate it with an explanatory example and compare its results with the results of the possibilistic MV model.

Keywords

Portfolio selection, Possibility theory, Triangular fuzzy numbers, Convex quadratic minimization, Expert knowledge, Possibilistic skewness

Project Number

Yok

References

• Ali MY., Sultana A., Khan AFMK. Comparison of fuzzy multiplication operation on triangular fuzzy number. IOSR Journal of Mathematics 2016; 12(4-I): 35-41.
• Carlsson C., Fullér R., Majlender P. A possibilistic approach to selecting portfolios with highest utility score. Fuzzy Sets and Systems 2002; 131(1): 13-21.
• Corazza M., Nardelli C. Possibilistic mean–variance portfolios versus probabilistic ones: the winner is. Decisions in Economics and Finance 2019; 42(1): 51-75.
• Fullér R., Mezei J., Várlaki P. An improved index of interactivity for fuzzy numbers. Fuzzy Sets and Systems 2011; 165(1), 50-60.
• Gill PE., Wong E. Methods for convex and general quadratic programming. Mathematical Programming Computation 2015; 7(1): 71-112.
• Goldfarb D., Iyengar G. Robust portfolio selection problems. Mathematics of Operations Research 2003; 28(1): 1-38.
• Gong X., Min L., Yu C.. Multi-period portfolio selection under the coherent fuzzy environment with dynamic risk-tolerance and expected-return levels. Applied Soft Computing 2022; 114: 108104.
• Göktaş F., Duran A. A new possibilistic mean-variance model based on the principal components analysis: an application on the Turkish Holding Stocks. Journal of Multiple-Valued Logic & Soft Computing 2019; 32(5-6): 455-476.
• Göktaş F., Duran A. Olabilirlik ortalama–varyans modelinin matematiksel analizi. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 2020; 22(1): 80-91.
• Gupta P., Mehlawat MK., Yadav S., Kumar A. Intuitionistic fuzzy optimistic and pessimistic multi-period portfolio optimization models. Soft Computing 2020; 24(16): 11931-11956.
• Li X., Guo S., Yu L. Skewness of fuzzy numbers and its applications in portfolio selection. IEEE Transactions on Fuzzy Systems 2015; 23(6): 2135-2143.
• Markowitz H. Portfolio selection. The Journal of Finance 1952; 7(1): 77-91.
• Pasha E., Saeidifar A., Asady B. The percentiles of fuzzy numbers and their applications. Iranian Journal of Fuzzy Systems 2009; 6(1): 27-44.
• Tanaka H., Guo P. Portfolio selection based on upper and lower exponential possibility distributions. European Journal of Operational Research 1999; 114(1): 115-126.
• Tanaka H., Guo P., Türksen IB. Portfolio selection based on fuzzy probabilities and possibility distributions. Fuzzy Sets and Systems 2000; 111(3): 387-397.
• Taş O., Kahraman C., Güran CB. A scenario based linear fuzzy approach in portfolio selection problem: application in the Istanbul Stock Exchange. Journal of Multiple-Valued Logic & Soft Computing 2016; 26(3-5): 269-294.
• Tütüncü RH., Koenig M. Robust asset allocation. Annals of Operations Research 2004; 132(1): 157-187.
• Yang XY., Chen SD., Liu WL., Zhang, Y. A multi-period fuzzy portfolio optimization model with short selling constraints. International Journal of Fuzzy Systems 2022; 24(6): 2798–2812.
• Zhang WG. Possibilistic mean–standard deviation models to portfolio selection for bounded assets. Applied Mathematics and Computation 2007; 189(2): 1614-1623.
• Zhang WG., Wang YL., Chen ZP., Nie ZK. Possibilistic mean-variance models and efficient frontiers for portfolio selection problem. Information Sciences 2007; 177(13): 2787–2801.
• Zhang WG., Zhang XL., Xiao WL. Portfolio selection under possibilistic mean–variance utility and a SMO algorithm. European Journal of Operational Research 2009; 197(2): 693-700.