Skip to main content

Portfolio Selection with Possibilistic Kurtosis

  • Conference paper

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 125))

Abstract

This paper proposes a new approach for modeling multiple objective portfolio selection problem by applying weighted possibilistic moments of trapezoidal fuzzy numbers. The proposed model allows the decision-maker to select the suitable portfolio taking into account the impreciseness to the market scenarios. Here, the objectives are to (i) maximize the expected portfolio return, (ii) minimize the portfolio variance, (iii) maximize the portfolio skewness, and (iv) minimize the portfolio kurtosis for the risky investor. The proposed model has been solved by Zimmermann’s fuzzy goal programming technique. The model is illustrated by a numerical example using data extracted from the Bombay Stock Exchange.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Samuelson, P.: The fundamental approximation theorem of portfolio analysis in terms of means, variances an higher moments. Rev. Econ. Stud. 25, 65–86 (1958)

    Article  Google Scholar 

  2. Bhattacharyya, R., Kar, M.B., Kar, S., Dutta Majumder, D.: Mean- entropy—skewness fuzzy portfolio selection by credibility theory approach. Chaudhury, S. et al. (Eds.) In: PReMI LNCS 5909, pp. 603–608 (2009)

    Google Scholar 

  3. Bhattacharyya, R., Kar, S., Dutta Majumder, D.: Fuzzy mean-variance-skewness portfolio selection models by interval analysis. Comput. Math. Appl. 61, 126–137 (2011)

    Article  MathSciNet  Google Scholar 

  4. Bhattacharyya, R., Kar, S.: Possibilistic mean-variance-skewness portfolio selection models. Int. J. Oper. Res. 8, 44–56 (2011)

    MathSciNet  Google Scholar 

  5. Bhattacharyya, R., Kar, S.: Multi-objective fuzzy optimization for portfolio selection: an embedding theorem approach. Turk. J. Fuzzy Syst. 2, 14–35 (2011)

    Google Scholar 

  6. Markowitz, H.: Portfolio selection. J. Financ. 7, 77–91 (1952)

    Google Scholar 

  7. Davies, R., Kat, H., Lu S.: Fund of hedge funds portfolio selection: a multiple objective approach. Working Paper, ISMA Center (2004)

    Google Scholar 

  8. Berenyi, Z.: Performance of leveraged assets funds., Working Paper University of Mnich (2001)

    Google Scholar 

  9. Berenyi, Z.: Measuring hedges funds, risk with moment based variance-equivalent measures. In: Adcock- Jurczenko-Maillet (ed.) Multi Moment Asset Pricing Models and Related Topic, Springer, New York (2005)

    Google Scholar 

  10. Huang, X.: Mean-semivariance models for fuzzy portfolio selection. J. Comput. Appl. Math. 217(1), 1–8 (2008)

    Article  MathSciNet  Google Scholar 

  11. Li, X., Qin, Z., Kar, S.: Mean-variance-skewness model for portfolio selection with fuzzy returns. Eur. J. Oper. Res. 202(1), 239–247 (2010)

    Article  Google Scholar 

  12. Louis, A.F., Jules, S.K., Christian, D.T.: Kurtosis and Semi-kurtosis for Portfolios Selection with Fuzzy Returns. In: Int. Statistical Inst. Proceedings of the 58th World Statistical Congress, Dublin (Session CPS027) (2011)

    Google Scholar 

  13. Zimmermann, H.J.: Fuzzy Linear Programming with several objective functions. Fuzzy Sets Syst. 1, 46–55 (1978)

    Article  MathSciNet  Google Scholar 

  14. Bellman, R.E., Zadeh, L.A.: Decision-making in a fuzzy environment. Manag. Sci. 17(4), 141–164 (1970)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sheikh Ahmed Hossain .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer India

About this paper

Cite this paper

Hossain, S.A., Bhattacharyya, R. (2015). Portfolio Selection with Possibilistic Kurtosis. In: Chakraborty, M.K., Skowron, A., Maiti, M., Kar, S. (eds) Facets of Uncertainties and Applications. Springer Proceedings in Mathematics & Statistics, vol 125. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2301-6_23

Download citation

Publish with us

Policies and ethics