ijier logo

A comparison of the Normal and Laplace distributions in the models of fuzzy probability distribution for portfolio selection

Authors
Keywords:
Array, Array, Array
Abstract

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.

Author Biography
  1. Benjamin Bedregal, Federal University of Rio Grande do Norte

    Departamento de Informática e Matemática Aplicada da

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
2020-05-01
Section
Journal Articles
License

Copyright (c) 2020 Marcus Pinto da Costa da Rocha, Lucelia M. Lima, Valcir J. C. Farias, Benjamin Bedregal, Heliton R. Tavares

Creative Commons License

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

Pinto da Costa da Rocha, M., Lima, L. M., Farias, V. J. C., Bedregal, B., & Tavares, H. R. (2020). A comparison of the Normal and Laplace distributions in the models of fuzzy probability distribution for portfolio selection. International Journal for Innovation Education and Research, 8(5), 183-198. https://doi.org/10.31686/ijier.vol8.iss5.2332