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A Novel Game-Theoretical Approach for The Possibilistic Mean - Variance Model

Yıl 2024, Cilt: 12 Sayı: 1, 1 - 12, 20.07.2024

Furkan Göktaş

https://doi.org/10.17093/alphanumeric.1244061

Öz

Possibility theory is a significant tool to deal with the imprecise probability and benefit from the expert knowledge. Thus, the possibilistic mean - variance (MV) model is a considerable alternative for the portfolio selection problem. In this study, we propose an extension of the possibilistic MV model to the multiple market strategies where we assume that the possibility distributions of asset returns are given with triangular fuzzy numbers. The proposed extension, which is related to the game theory is given with a linear optimization problem. Thus, it can be solved with the Simplex algorithm as in this study. After giving the theoretical points, we illustrate it by using a numerical example. To the best of our knowledge, this is the first paper bringing the game theory and the possibilistic MV model together.

Anahtar Kelimeler

Fuzzy Logic Game Theory Linear Optimization Portfolio Selection Possibility Theory

Kaynakça

  • Carlsson, C., & Fullér, R. (2001). On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets and Systems, 122(2), 315–326. https://doi.org/10.1016/s0165-0114(00)00043-9
  • 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. 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. https://doi.org/10.1007/s10203-019-00234-1
  • Dubois, D. (2006). Possibility theory and statistical reason-ing. Computational Statistics & Data Analysis, 51(1), 47–69. https://doi.org/10.1016/j.csda.2006.04.015
  • Fullér, R., & Harmati, I. Á. (2017). On Possibilistic Dependencies: A Short Survey of Recent Developments. In Studies in Fuzziness and Soft Computing (pp. 261–273). Springer International Publishing. https://doi.org/10.1007/978-3-319-64286-4_16
  • Goldfarb, D., & Iyengar, G. (2003). Robust Portfolio Selection Problems. Mathematics of Operations Research, 28(1), 1–1. https://doi.org/10.1287/moor.28.1.1.14260
  • Göktaş, F. (2024). The Possibilistic Mean-Variance Model with Uncertain Possibility Distributions. Mehmet Akif Ersoy Üniversitesi İktisadi Ve İdari Bilimler Fakültesi Dergisi. https://doi.org/10.30798/makuiibf.1389261
  • Göktaş, F., & Duran, A. (2020). Olabilirlik ortalama – varyans modelinin matematiksel analizi. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 22(1), 80–91. https://doi.org/10.25092/baunfbed.677022
  • Jiao, H., & Li, B. (2022). Solving min–max linear fractional programs based on image space branch-and-bound scheme. Chaos, Solitons & Fractals, 164, 112682–1. https://doi.org/10.1016/j.chaos.2022.112682
  • Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77–91. https://doi.org/10.1111/j.1540-6261.1952.tb01525.x
  • Raghavan, T. (1994). Zero-sum two-person games. In Hand- book of Game Theory with Economic Applications (Vol. 2, pp. 735–768). Elsevier. https://doi.org/10.1016/S1574-0005(05)80052-9
  • 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. https://doi.org/10.1016/s0165-1889(99)00088-3
  • Sikalo, M., Arnaut-Berilo, A., & Zaimovic, A. (2022). Efficient Asset Allocation: Application of Game Theory-Based Model for Superior Performance. International Journal of Financial Studies, 10(1), 20–21. https://doi.org/10.3390/ijfs10010020
  • Souliotis, G., Alanazi, Y., & Papadopoulos, B. (2022). Construction of Fuzzy Numbers via Cumulative Distribution Function. Mathematics, 10(18), 3350–3351. https://doi.org/10.3390/math10183350
  • 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. Tütüncü, R., & Koenig, M. (2004). Robust Asset Allocation. Annals of Operations Research, 132(1–4), 157–187. https://doi.org/10.1023/b:anor.0000045281.41041.ed
  • Young, M. R. (1998). A Minimax Portfolio Selection Rule with Linear Programming Solution. Management Science, 44(5), 673–683. https://doi.org/10.1287/mnsc.44.5.673
  • 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. https://doi.org/10.1016/j.ejor.2008.07.011
  • Zhang, Y., Li, X., & Guo, S. (2017). Portfolio selection problems with Markowitz's mean–variance framework: a review of literature. Fuzzy Optimization and Decision Making, 17(2), 125–158. https://doi.org/10.1007/s10700-017-9266-z

Yıl 2024, Cilt: 12 Sayı: 1, 1 - 12, 20.07.2024

Furkan Göktaş

https://doi.org/10.17093/alphanumeric.1244061

Öz

Kaynakça

  • Carlsson, C., & Fullér, R. (2001). On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets and Systems, 122(2), 315–326. https://doi.org/10.1016/s0165-0114(00)00043-9
  • 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. 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. https://doi.org/10.1007/s10203-019-00234-1
  • Dubois, D. (2006). Possibility theory and statistical reason-ing. Computational Statistics & Data Analysis, 51(1), 47–69. https://doi.org/10.1016/j.csda.2006.04.015
  • Fullér, R., & Harmati, I. Á. (2017). On Possibilistic Dependencies: A Short Survey of Recent Developments. In Studies in Fuzziness and Soft Computing (pp. 261–273). Springer International Publishing. https://doi.org/10.1007/978-3-319-64286-4_16
  • Goldfarb, D., & Iyengar, G. (2003). Robust Portfolio Selection Problems. Mathematics of Operations Research, 28(1), 1–1. https://doi.org/10.1287/moor.28.1.1.14260
  • Göktaş, F. (2024). The Possibilistic Mean-Variance Model with Uncertain Possibility Distributions. Mehmet Akif Ersoy Üniversitesi İktisadi Ve İdari Bilimler Fakültesi Dergisi. https://doi.org/10.30798/makuiibf.1389261
  • Göktaş, F., & Duran, A. (2020). Olabilirlik ortalama – varyans modelinin matematiksel analizi. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 22(1), 80–91. https://doi.org/10.25092/baunfbed.677022
  • Jiao, H., & Li, B. (2022). Solving min–max linear fractional programs based on image space branch-and-bound scheme. Chaos, Solitons & Fractals, 164, 112682–1. https://doi.org/10.1016/j.chaos.2022.112682
  • Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77–91. https://doi.org/10.1111/j.1540-6261.1952.tb01525.x
  • Raghavan, T. (1994). Zero-sum two-person games. In Hand- book of Game Theory with Economic Applications (Vol. 2, pp. 735–768). Elsevier. https://doi.org/10.1016/S1574-0005(05)80052-9
  • 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. https://doi.org/10.1016/s0165-1889(99)00088-3
  • Sikalo, M., Arnaut-Berilo, A., & Zaimovic, A. (2022). Efficient Asset Allocation: Application of Game Theory-Based Model for Superior Performance. International Journal of Financial Studies, 10(1), 20–21. https://doi.org/10.3390/ijfs10010020
  • Souliotis, G., Alanazi, Y., & Papadopoulos, B. (2022). Construction of Fuzzy Numbers via Cumulative Distribution Function. Mathematics, 10(18), 3350–3351. https://doi.org/10.3390/math10183350
  • 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. Tütüncü, R., & Koenig, M. (2004). Robust Asset Allocation. Annals of Operations Research, 132(1–4), 157–187. https://doi.org/10.1023/b:anor.0000045281.41041.ed
  • Young, M. R. (1998). A Minimax Portfolio Selection Rule with Linear Programming Solution. Management Science, 44(5), 673–683. https://doi.org/10.1287/mnsc.44.5.673
  • 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. https://doi.org/10.1016/j.ejor.2008.07.011
  • Zhang, Y., Li, X., & Guo, S. (2017). Portfolio selection problems with Markowitz's mean–variance framework: a review of literature. Fuzzy Optimization and Decision Making, 17(2), 125–158. https://doi.org/10.1007/s10700-017-9266-z
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Yöneylem
Bölüm Makaleler
Yazarlar

Furkan Göktaş 0000-0001-9291-3912

Yayımlanma Tarihi 20 Temmuz 2024
Gönderilme Tarihi 29 Ocak 2023
Yayımlandığı Sayı Yıl 2024 Cilt: 12 Sayı: 1

Kaynak Göster

APA Göktaş, F. (2024). A Novel Game-Theoretical Approach for The Possibilistic Mean - Variance Model. Alphanumeric Journal, 12(1), 1-12. https://doi.org/10.17093/alphanumeric.1244061
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