Geodesic
Investigation of the minimum risk portfolio under conditions of hybrid uncertainty based on the weakest $t$-norm
Nečetkie sistemy i mâgkie vyčisleniâ, Tome 13 (2018) no. 2, pp. 101-112.

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A model of a minimum risk portfolio under conditions of a hybrid uncertainty of a possibilistic-probabilistic type was developed and investigated. The peculiarity of the model is that interaction of fuzzy parameters in it is described by the weakest triangular norm ($t$-norm). A formula for the portfolio variance is obtained, which allows to estimate its risk. The model of feasible portfolios is based on the principle of expected possibility. Its application leads to the removal of possibilistic uncertainty by imposing requirements on the possibility / necessity of meeting the investor's requirements for an acceptable level of portfolio return. An equivalent crisp analog of the model is constructed and demonstrated on a numerical example. Obtained results allow us to build generalized models of portfolio optimization problems with prime objective on processing a hybrid (combined) type of uncertainty.
Keywords: minimum risk portfolio, hybrid uncertainty, weakest $t$-norm, possibility, necessity, risk, profitability. 
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A. V. Yazenin; I. S. Soldatenko. Investigation of the minimum risk portfolio under conditions of hybrid uncertainty based on the weakest $t$-norm. Nečetkie sistemy i mâgkie vyčisleniâ, Tome 13 (2018) no. 2, pp. 101-112. http://geodesic.mathdoc.fr/item/FSSC_2018_13_2_a0/

[1] Yazenin A. V., Egorova Yu. E., “On solution methods for tasks of possibilistic-probabilistic optimization”, Herald of Tver State University. Series: Applied Mathematics, 2013, no. 4 (31), 85–103 (in Russian)

[2] Egorova Yu. E., Yazenin A. V., “Parameter identification for possibilistic distribution of expected values of fuzzy random variables Tw-sums”, Herald of Tver State University. Series: Applied Mathematics, 2014, no. 2, 81–93 (in Russian) | MR

[3] Egorova Yu. E., Yazenin A. V., “Stochastic quasi-gradient method for solving possibilistic-probabilistic optimization task of one class”, Herald of Tver State University. Series: Applied Mathematics, 2014, no. 4, 57–70 (in Russian)

[4] Luhandjula M. K., “Optimisation under hybrid uncertainty”, Fuzzy Sets and Systems, 146:2 (2004), 187–203 | DOI | MR | Zbl

[5] Nahmias S., “Fuzzy variables”, Fuzzy Sets and Systems, 1:2 (1978), 97–110 | DOI | MR | Zbl

[6] Nahmias S., “Fuzzy variables in a random environment”, Advances in Fuzzy Set Theory and Applications, eds. M.M. Gupta, R.K. Ragade, R.R. Yager, North-Holland, Amsterdam, 1979, 165–180 | MR

[7] Yazenin A. V., Basic concepts of the theory of possibilities. Mathematical decision-making apparatus in a hybrid uncertainty, Fizmatlit Publ., Moscow, 2016, 144 pp. (in Russian)

[8] Feng Y., Hu L., Shu H., “The variance and covariance of fuzzy random variables and their applications”, Fuzzy Sets and Systems, 120:3 (2001), 487–497 | DOI | MR | Zbl

[9] Dubois D., Prade H., Theorie des Possibilites, Application a la Representation des Connaissances en Informatique, Masson, Paris, 1988 | MR | MR

[10] Nguyen H. T., Walker E. A., A First Course in Fuzzy Logic, CRC Press, Boca Raton, 1997 | MR | Zbl

[11] Khokhlov M. Yu., Yazenin A. V., “Calculation of numerical characteristics of fuzzy random variables”, Herald of Tver State University. Series: Applied Mathematics, 2003, no. 1, 39–43 (in Russian) | MR

[12] Hong D. H., “Parameter estimations of mutually t-related fuzzy variables”, Fuzzy Sets and Systems, 123:1 (2001), 63–71 | DOI | MR | Zbl

[13] Ermolev Yu. M., Stochastic programming methods, Nauka Publ., Moscow, 1976 (in Russian)

[14] Uryasev S. P., Adaptive algorithms for stochastic optimization and game theory, Nauka Publ., Moscow, 1990 (in Russian) | MR

[15] Markowitz H., “Portfolio Selection”, The Journal of Finance, 7:1 (1952), 77–91 | DOI | MR

[16] Yazenin A. V., “Possibilistic–Probabilistic Models and Methods of Portfolio Optimization”, Perception-based Data Mining and Decision Making in Economics and Finance, v. 36, Studies in Computational Intelligence, eds. I. Batyrshin, J. Kacprzyk, L. Sheremetov, L.A. Zadeh, Springer, Berlin, Heidelberg, 2007, 241–259 | DOI | Zbl