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Portfolio optimization based on fuzzy entropy

  • Mohamadtaghi Rahimi
  • Pranesh Kumar
Original paper
  • 5 Downloads

Abstract

In this paper, a general solution is presented for portfolio optimization in a situation where the expressed prices are estimated as fuzzy numbers. To reach the solution, the expected returns, semi-variance, skewness, semi-kurtosis and semi-entropy are considered with this assumption that the portfolio returns are asymmetric. In this method, all the data about the expected returns are considered and no expected return value is ignored just because of a little growth of risk. We have the conclusion by discussing an illustrative example to verify the developed approach.

Keywords

Portfolio optimization Semi-entropy Genetic algorithm Regression line 

Notes

References

  1. 1.
    Markowitz, H.: Portfolio selection. J. Finance 7, 77–91 (1952)Google Scholar
  2. 2.
    Grauer, R.R., Hakansson, N.H.: On the use of mean-variance and quadratic approximations in implementing dynamic investment strategies: a comparison of returns and investment policies. Manag. Sci. 39, 856–871 (1993)CrossRefGoogle Scholar
  3. 3.
    Li, D., Ng, W.L.: Optimal dynamic portfolio selection: multi-period mean-variance formulation. Math. Finance 10, 387–406 (2000)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Wei, S.Z., Ye, Z.X.: Multi-period optimization portfolio with bankruptcy control in stochastic market. Appl. Math. Comput. 186, 414–425 (2007)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Calafiore, G.C.: Multi-period portfolio optimization with linear control policies. Automatica 44, 2463–2473 (2008)CrossRefGoogle Scholar
  6. 6.
    Yu, J.R., Lee, W.Y.: Portfolio rebalancing model using multiple criteria. Eur. J. Oper. Res. 209, 166–175 (2011)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Rahimi, M., Kumar, P., Yari, G.: Portfolio selection using ant colony algorithm and entropy optimization. Pak. J. Stat. 33, 441–448 (2017)MathSciNetGoogle Scholar
  8. 8.
    Liu, B., Liu, Y.K.: Expected value of fuzzy variable and fuzzy expected value models. IEEE Trans. Fuzzy Syst. 10, 445–450 (2002)CrossRefGoogle Scholar
  9. 9.
    Li, X., Liu, B.: A sufficient and necessary condition for credibility measures. Int. J. Uncertain. Fuzz. Knowl Based Syst. 14, 527–535 (2006)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Li, P., Liu, B.: Entropy of credibility distributions for fuzzy variables. IEEE Trans. Fuzzy Syst. 16, 123–129 (2000)Google Scholar
  11. 11.
    Yari, G., Rahimi, M., Moomivand, B., Kumar, P.: Credibility based fuzzy entropy measure. Aust. J. Math. Anal. Appl. 13, 1–7 (2016)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Rahimi, M., Kumar, P., Yari, G.: Credibility measure for intuitionistic fuzzy variables. Mathematics 6(4), 50–56 (2018)CrossRefGoogle Scholar
  13. 13.
    Kundu, T., Islam, S.: A new interactive approach to solve entropy based fuzzy reliability optimization model. Int. J. Interact. Des. Manuf. (2018).  https://doi.org/10.1007/s12008-018-0484-6 CrossRefGoogle Scholar
  14. 14.
    Chen, R.: Fuzzy dual experience-based design evaluation model for integrating engineering design into customer responses. Int. J. Interact. Des. Manuf. 10, 439 (2016).  https://doi.org/10.1007/s12008-016-0310-y CrossRefGoogle Scholar
  15. 15.
    Yari, G., Sajedi, A., Rahimi, M.: Portfolio selection in the credibilistic framework using Renyi entropy and Renyi cross entropy. Int. J. Fuzzy Log. Intel. Sys. 18(1), 78–83 (2018)CrossRefGoogle Scholar
  16. 16.
    Yari, G., Rahimi, M., Kumar, P.: Multi-period multi-criteria (MPMC) valuation of American options based on entropy optimization principles. Iran. J. Sci. Technol. Trans. A Sci. 41, 81–86 (2017)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Song, H.S., Rhee, H.K., Kim, J.H., Lee, J.H.: Reading children’s emotions based on the fuzzy inference and theories of chromotherapy. Information 19, 735–742 (2016)Google Scholar
  18. 18.
    Farnoosh, R., Rahimi, M., Kumar, P.: Removing noise in a digital image using a new entropy method based on intuitionistic fuzzy sets. In: 2016 IEEE International Conference on Fuzzy (FUZZ-IEEE), Vancouver, BC, Canada, pp. 24–29 (2016). http://dx.doi.org/10.1109/FUZZ-IEEE.2016.7737843
  19. 19.
    Zadeh, L.A.: Fuzzy set as basis for a theory of possibility. Fuzzy Set. Syst. 1(1), 3–28 (1978)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Mandal, S., Maitya, K., Mondal, S., Maiti, M.: Optimal production inventory policy for defective items with fuzzy time period. Appl. Math. Model. 34(8), 10–822 (2010)MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag France SAS, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of Northern British ColumbiaPrince GeorgeCanada

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