A comparison of the Normal and Laplace distributions in the models of fuzzy probability distribution for portfolio selection
DOI:
https://doi.org/10.31686/ijier.vol8.iss5.2332Keywords:
Fuzzy number, VaR, Portfolio selectionAbstract
The propose of this work is applied the fuzzy Laplace distribution on a possibilistic mean-variance model presented by Li et al which appliehe fuzzy normal distribution. The theorem necessary to introduce the Laplace distribution in the model was demonstrated. It was made an analysis of the behavior of the fuzzy normal and fuzzy Laplace distributions on the portfolio selection with VaR constraint and risk-free investment considering real data. The results showns that were not difference in assets selection and in return rate, however, There was a change in the risk rate, which was higher in the Laplace distribution than in the normal distribution.
References
Alexander, G. J., Baptista, A. M., 2002. Economic implications of using a mean-VaR model for portfolio selection: a comparison with mean-variance analisys. Journal of Economic Dynamics and Control 26, 1159-1193. DOI: https://doi.org/10.1016/S0165-1889(01)00041-0
Asmus, Tiago da Cruz, Dimuro, Grac{c}aliz Pereira, Bedegral, Benjamin: On Two-Player Interval-Valued Fuzzy Bayesian Games. Int. J. Intell. Syst. 32(6): 557-596 (2017). DOI: https://doi.org/10.1002/int.21857
Buckley, J.J. Fuzzy Probabilities: A New Approach and Applications. Springer, Berlin, (2005).
Carlsson, C., Fuller, R., 2001. On possibilistic mean value and variance of fuzzy numbers. Fuzzy Sets and Systems 122, 315-326. DOI: https://doi.org/10.1016/S0165-0114(00)00043-9
Goestschel and Voxman, 1986. Elementary fuzzy calculus. Fuzzy Set and Systems, 18, 31-43. DOI: https://doi.org/10.1016/0165-0114(86)90026-6
Michael H.. Applied Fuzzy Arithmetic: An Introduction with Engineering Applications. Springer-Verlag Berlin Heidelberg, (2005).
Leon, T., Liem, V., Vercher, E., 2002. Viability of infeasible portfolio selection problems: a fuzzy approach. European Journal of Operational Research 139, 178-189. DOI: https://doi.org/10.1016/S0377-2217(01)00175-8
Li, T., Zhang, W., Xu, W., 2013. Fuzzy possibilistic portfolio selection model with VaR constraint and risk-free investiment. Economic Modeling 31, 12-17. DOI: https://doi.org/10.1016/j.econmod.2012.11.032
Markowitz,H., 1952. Portfolio selection. Journal of Finance 7, 77-91. DOI: https://doi.org/10.1111/j.1540-6261.1952.tb01525.x
Markowitz,H.. Portfolio selection. Efficient diversification of Investments. Willey, New York, (1959).
Ramaswamy, S.,1998. Portfolio selection using fuzzy decision theory. Working Paper of Bank for International Settlements, Nº 59.
Tanaka, H., Guo, P., Turksen, I. B., 2000. Portfolio selection based on fuzzy probabilities and possibility distributions. Fuzzy Sets and Systems 111, 387-397. DOI: https://doi.org/10.1016/S0165-0114(98)00041-4
Wang, S. Y., Zhu, S. S., 2002. On fuzzy portfolio selection problems. Fuzzy Optimization and Decision Making 1, 361-377. DOI: https://doi.org/10.1023/A:1020907229361
Wang, Wei and Zhenyuan Wang, 2014: Total orderings defined on the set of all fuzzy numbers. Fuzzy Sets and Systems, 243:131–141. DOI: https://doi.org/10.1016/j.fss.2013.09.005
Watada, J., 1997. Fuzzy portfolio selection and its applications to decision making. Tatra Mountains Mathematical Publication 13, 219-248.
Valvis, Emmanuel, 2009.: A new linear ordering of fuzzy numbers on subsets of F (R). Fuzzy Optimization and Decision Making, 8(2):141–163. DOI: https://doi.org/10.1007/s10700-009-9057-2
Xu, W. D., Wu, C. F., Xu, W. J., Li, H.Y., 2010. Dynamic asset allocation with jump risk. Journal of Risk 12, 29-44. DOI: https://doi.org/10.21314/JOR.2010.210
Xu, W. J., Xu, W. D., Li, H. Y., Zhang, W. G., 2010. Uncertainty portifolio model in cross currency markets. International Journal of Uncertainty. Fuzziness and Knowledge-Based Systems 18, 759-777. DOI: https://doi.org/10.1142/S0218488510006787
Zdenec, Zmeskal Z., 2005. Value at risk methodology of international index portfolio under soft conditions. International Review of Financial Analysis 14, 263-275. DOI: https://doi.org/10.1016/j.irfa.2004.06.011
Zhang, W. G., Nie, Z. K., 2003. On possibilistic variance of fuzzy numbers. Lecture Notes in Artificial Intelligence 2639, 398-402. DOI: https://doi.org/10.1007/3-540-39205-X_66
Zhang, W. G., Xiao, W. L., Xu, W. J., 2010. A possibilistic portifolio adjusting model with new added assets. Economic Modelling 27, 208-213. DOI: https://doi.org/10.1016/j.econmod.2009.08.008
Downloads
Published
Issue
Section
License
Copyright (c) 2020 Marcus Pinto da Costa da Rocha, Lucelia M. Lima, Valcir J. C. Farias, Benjamin Bedregal, Heliton R. Tavares
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.
Copyrights for articles published in IJIER journals are retained by the authors, with first publication rights granted to the journal. The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author for more visit Copyright & License.
How to Cite
Accepted 2020-05-02
Published 2020-05-01
Most read articles by the same author(s)
- Marcus Pinto da Costa da Rocha, Matheus Souza, Valcir Farias, Heliton Tavares, Optimization of soybean outflow routes from Mato Grosso, Brazil , International Journal for Innovation Education and Research: Vol. 8 No. 8 (2020): International Journal for Innovation Education and Research
- Valcir João da Cunha Farias, Marcus Pinto da Costa da Rocha, Lucélia M. Lima, Heliton Ribeiro Tavares, Optimization of filament antennas using the Gauss-Newton method , International Journal for Innovation Education and Research: Vol. 9 No. 7 (2021): International Journal for Innovation Education and Research