Квазиэффективная граница портфеля минимального риска в условиях гибридной неопределенности
Ключевые слова:
возможностно-вероятностная оптимизация, портфель минимального риска, гибридная неопределенность, сильнейшая t-норма, длинные продажи, квазиэффективная граница, мера возможности, мера необходимости
Аннотация
В статье разработан метод построения квазиэффективной границы портфеля минимального риска при запрещенных коротких продажах в условиях гибридной неопределенности возможностно-вероятностного типа. С этой целью построена обобщенная модель портфеля минимального риска. Для оценки риска инвестиционного портфеля используется дисперсия портфеля, определенная в четкой форме в соответствии с подходом Фенга. Модель допустимых портфелей рассмотрена в контексте возможность/необходимость. При построении ее эквивалентного детерминированного аналога использован принцип ожидаемой возможности. Полученные эквивалентные детерминированные аналоги обобщенной модели портфеля минимального риска, как в случае меры возможности, так и необходимости, являются задачами квадратичного программирования. Полученные в работе алгоритмы обработки возможностно-вероятностной информации для оценки параметров модели основаны на сдвиг-масштабном представлении нечеткой случайной величины. Возможности подхода демонстрируются на модельном примере с использованием реальных данных Российского финансового рынка.
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Литература
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24. Liu B. (2004) Uncertainty theory: an introduction to its axiomatic foundations. – Berlin : Springer.
25. Yazenin A. and Soldatenko I. (2018) A portfolio of minimum risk in a hybrid uncertainty of a possibilistic-probabilistic type: comparative study; eds. by J. Kacprzyk, E. Szmidt, S. Zadrozny, K. Atanassov, M. Krawczak. Advances in Fuzzy Logic and Technology 2017. Series: Advances in Intelligent Systems and Computing. Vol. 643. P. 551–563.
26. Soldatenko I. S. and Yazenin A. V. (2020) On one problem of portfolio analysis under soft constraints. Fuzzy Systems and Soft Computing. Vol. 15, No 1. P. 64–76. (in Russian) DOI
27. Yazenin A. V. and Soldatenko I. S. (2021) Model of a minimal risk portfolio under hybrid uncertainty. Control and Cybernetics. Vol. 50, No 2. P. 315–332.
28. Rogonov S. A., Soldatenko I. S. and Yazenin A. V. (2022) On the quasi-efficient frontier of the set of optimal portfolios under hybrid uncertainty with short sales allowed. Control & Cybernetics. Vol. 51, No 4. P. 327–341.
29. Yazenin A. V. (2016) Basic concepts of the theory of possibilities. Moscow : Fizmatlit Publ. (in Russian)
30. Yazenin A. V. and Wagenknecht M. (1996) Possibilistic Optimization. A measure-based approach. Cottbus, Germany : Brandenburgische Tecnische Universitat. 140 p.
31. Nguyen H. T. and Walker E. A. (1997) A First Course in Fuzzy Logic. – CRC Press, Boca Raton.
32. Feng Y., Hu L. and Shu H. (2001) The variance and covariance of fuzzy random variables and their applications. Fuzzy Sets and Systems. Vol. 120, No 3. P. 487–497.
33. Barbaumov V. E., Gladkikh I. M. and Chuyko A. S. (2003) Financial investments: textbook. Moscow : Publishing House of the Plekhanov Russian Academy of Economics. (in Russian)
2. Markowitz H. (1959) Portfolio Selection: Efficient Diversification of Investments. – New York: Wiley.
3. Zadeh L. A. (1965) Fuzzy sets. Information and Control. Vol. 8. P. 338–353.
4. Zadeh L. A. (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems. Vol. 1. P. 3–28.
5. Nahmias S. (1978) Fuzzy variables. Fuzzy Sets Systems. Vol. 1. P. 97–110.
6. Dubois D. and Prade H. (1988) Possibility theory. New York : Plenum Press.
7. Tanaka H., Guo P. and Turksen I. B. (2000) Portfolio selection based on fuzzy probabilities and possibility distributions. Fuzzy Sets and Systems. Vol. 111. P. 387–397.
8. Inuiguchi M. and Tanino T. (2000) Portfolio selection under independent possibilistic information. Fuzzy Sets and Systems. Vol. 115. P. 83–92.
9. Parra M. A., Terol A. B. and Uría M. V. R. (2001) A fuzzy goal programming approach to portfolio selection. European Journal of Operational Research. Vol. 133. P. 287–297.
10. Ammar E. and Khalifa H. A. (2003) Fuzzy portfolio optimization a quadratic programming approach. Chaos, Solitons and Fractals. Vol. 18, No 5. P. 1045–1054.
11. Zhang W. G. and Nie Z. K. (2004) On admissible efficient portfolio selection problem. Applied Mathematics and Computation. Vol. 159. P. 357–371.
12. Bilbao-Terol A. [et al.] (2006) Fuzzy compromise programming for portfolio selection. Applied Mathematics and Computation. Vol. 173, No 1. P. 251–264.
13. Giove S., Funari S. and Nardelli C. (2006) An interval portfolio selection problem based on regret function. European Journal of Operational Research. Vol. 170, No 1. P. 253–264.
14. Vercher E. (2008) Portfolios with fuzzy returns: Selection strategies based on semi-infinite programming. Journal of Computational and Applied Mathematics. Vol. 217. P. 381–393.
15. Kwakernaak H. (1978) Fuzzy random variables. Information Science. Vol. 15. P. 1–29.
16. Nahmias S. (1979) Fuzzy variables in a random environment; eds. by M. M. Gupta, R. K. Ragade, R. R. Yager. Advances in Fuzzy Sets Theory and Applications. – Amsterdam: NHPC. P. 165–180.
17. Yazenin A. V. (1992) Linear programming with random fuzzy data. Soviet J. Comput. Syst. Sci. Vol. 30. P. 86–93.
18. Liu B. (2002) Theory and practice of uncertain programming. Heidelberg : Physica.
19. Luhandjula M. K. (2004) Optimisation under hybrid uncertainty. Fuzzy Sets and Systems. Vol. 146. P. 187–203.
20. Li J., Xu J. P. and Gen M. (2006) A class of fuzzy random multiobjective programming problem. Mathematical and Computer Modelling. Vol. 44. P. 1097–1113.
21. Yazenin A. V. (2004) Optimization with fuzzy random data and its application in financial analysis; eds. by I. Batyrshin, J. Kacprzyk, L. Sheremetov. Proceedings of International Conference on Fuzzy Sets and Soft Computing in Economics and Finance. SPb.
22. Yazenin A. V. (2007) Possibilistic-Probabilistic Models and Methods of Portfolio Optimization; eds. by I. Batyrshin, J. Kacprzyk, L. Sheremetov, L. A. Zadeh. Perception-based Data Mining and Decision Making in Economics and Finance, Studies in Computational Intelligence. Berlin, Heidelberg: Springer. P. 241–259.
23. Huang X. (2007) Two new models for portfolio selection with stochastic returns taking fuzzy information. European Journal of Operational Research. Vol. 180, No 1. P. 396–405.
24. Liu B. (2004) Uncertainty theory: an introduction to its axiomatic foundations. – Berlin : Springer.
25. Yazenin A. and Soldatenko I. (2018) A portfolio of minimum risk in a hybrid uncertainty of a possibilistic-probabilistic type: comparative study; eds. by J. Kacprzyk, E. Szmidt, S. Zadrozny, K. Atanassov, M. Krawczak. Advances in Fuzzy Logic and Technology 2017. Series: Advances in Intelligent Systems and Computing. Vol. 643. P. 551–563.
26. Soldatenko I. S. and Yazenin A. V. (2020) On one problem of portfolio analysis under soft constraints. Fuzzy Systems and Soft Computing. Vol. 15, No 1. P. 64–76. (in Russian) DOI
27. Yazenin A. V. and Soldatenko I. S. (2021) Model of a minimal risk portfolio under hybrid uncertainty. Control and Cybernetics. Vol. 50, No 2. P. 315–332.
28. Rogonov S. A., Soldatenko I. S. and Yazenin A. V. (2022) On the quasi-efficient frontier of the set of optimal portfolios under hybrid uncertainty with short sales allowed. Control & Cybernetics. Vol. 51, No 4. P. 327–341.
29. Yazenin A. V. (2016) Basic concepts of the theory of possibilities. Moscow : Fizmatlit Publ. (in Russian)
30. Yazenin A. V. and Wagenknecht M. (1996) Possibilistic Optimization. A measure-based approach. Cottbus, Germany : Brandenburgische Tecnische Universitat. 140 p.
31. Nguyen H. T. and Walker E. A. (1997) A First Course in Fuzzy Logic. – CRC Press, Boca Raton.
32. Feng Y., Hu L. and Shu H. (2001) The variance and covariance of fuzzy random variables and their applications. Fuzzy Sets and Systems. Vol. 120, No 3. P. 487–497.
33. Barbaumov V. E., Gladkikh I. M. and Chuyko A. S. (2003) Financial investments: textbook. Moscow : Publishing House of the Plekhanov Russian Academy of Economics. (in Russian)
Опубликован
2024-02-05
Как цитировать
Рогонов, С. А., Солдатенко, И. С., & Язенин, А. В. (2024). Квазиэффективная граница портфеля минимального риска в условиях гибридной неопределенности. Вестник ВГУ. Серия: Системный анализ и информационные технологии, (4), 92-103. https://doi.org/10.17308/sait/1995-5499/2023/4/92-103
Раздел
Системный анализ социально-экономических процессов
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