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Fuzzy Portfolio Diversification with Ordered Fuzzy Numbers

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Book cover Artificial Intelligence and Soft Computing (ICAISC 2017)

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Abstract

In this paper, we consider a multi-objective portfolio diversification problem under real constraints in fuzzy environment, where the objective is to minimize the variance of portfolio and maximize expected return rate of portfolio. The return rates of assets are modeled using concept of Ordered Fuzzy Candlesticks, which are Ordered Fuzzy Numbers. The use of them allows modeling uncertainty associated with financial data based on high-frequency data. Thanks to well-defined arithmetic of Ordered Fuzzy Numbers, the estimators of fuzzy-valued expected value and covariance can be computed in the same way as for real random variables. In an empirical study, 20 assets included in the Warsaw Stock Exchange Top 20 Index are used to compare considered fuzzy model with crisp mean-variance model.

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Notes

  1. 1.

    For Ordered Fuzzy Number which can be represented as classical convex fuzzy number.

References

  1. Carlsson, C., Fuller, R., Majlender, P.: A possibilistic approach to selecting portfolios with highest utility score. Fuzzy Sets Syst. 131, 13–21 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  2. Dubois, D., Prade, H.: Fuzzy Sets and Systems: Theory and Application. Academic Press, New York (1980)

    MATH  Google Scholar 

  3. Długosz, A., Jarosz, P.: Multiobjective optimization of electrothermal microactuators by means of Immune Game Theory Multiobjective Algorithm. In: Kleiber, M., et al. (eds.) Advances in Mechanics: Theoretical, Computational and Interdisciplinary Issues, pp. 141–145. Taylor & Francis Group, London (2016)

    Chapter  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  5. Jarosz, P., Burczyski, T.: Coupling of immune algorithms and game theory in multiobjective optimization. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2010. LNCS (LNAI), vol. 6114, pp. 500–507. Springer, Heidelberg (2010). doi:10.1007/978-3-642-13232-2_61

    Chapter  Google Scholar 

  6. Jarosz, P., Burczyński, T.: Biologically-inspired Methods and Game Theory in Multi-criterion Decision Processes. In: Bouvry, P., et al. (eds.) Intelligent Decision Systems in Large-Scale Distributed Environments, Studies in Computational Intelligence 362, pp. 101–124. Springer, Heidelberg (2011)

    Google Scholar 

  7. Konno, H., Yamazaki, H.: Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Manage. Sci. 37, 519–531 (1991)

    Article  Google Scholar 

  8. Konno, H., Shirakawa, H., Yamazaki, H.: A mean-absolute deviation-skewness portfolio optimization model. Ann. Oper. Res. 45, 205–220 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kosiński, W., Prokopowicz, P., Ślȩzak, D.: Drawback of fuzzy arithmetic - new intuitions and propositions. In: Burczyński, T., Cholewa, W., Moczulski, W. (eds.) Proceedings PACM, Methods of Artificial Intelligence, Gliwice, pp. 231–237 (2002)

    Google Scholar 

  10. Kosiński, W., Prokopowicz, P., Ślȩzak, D.: On algebraic operations on fuzzy numbers. In: Klopotek, M., Wierzchoń, S.T., Trojanowski, K. (eds.) Intelligent Information Processing and Web Mining, pp. 353–362. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  11. Kosiński, W., Prokopowicz, P., Ślȩzak, D.: Ordered fuzzy numbers. Bull. Polish Acad. Sci. Ser. Sci. Math. 51(3), 327–338 (2003)

    MathSciNet  MATH  Google Scholar 

  12. Kosiński, W., Prokopowicz, P.: Algebra of fuzzy numbers mathematica applicanda. J. Polish Math. Soc. 32(46/05), 37–63 (2004)

    Google Scholar 

  13. Kosiński, W.: On soft computing and modelling. Image Process. Commun. 11(1), 71–82 (2006)

    Google Scholar 

  14. Kosiński, W., Frischmuth, K., Wilczyńska-Sztyma, D.: A new fuzzy approach to ordinary differential equations. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2010. LNCS (LNAI), vol. 6113, pp. 120–127. Springer, Heidelberg (2010). doi:10.1007/978-3-642-13208-7_16

    Chapter  Google Scholar 

  15. Liu, B., Liu, Y.-K.: Expected value of fuzzy variable and fuzzy expected value models. IEEE Trans. Fuzzy Syst. 10, 445–450 (2002)

    Article  Google Scholar 

  16. Liu, Y.-K., Liu, B.: Fuzzy random variables: a scalar expected value operator. Fuzzy Optim. Decis. Making 2, 143–160 (2003). Kluwer Academic Publishers, Printed in The Netherlands

    Article  MathSciNet  Google Scholar 

  17. Markowitz, H.M.: Portfolio selection. J. Financ. 7(1), 77–91 (1952)

    Google Scholar 

  18. Markowitz, H.M.: Portfolio selection: efficient diversification of investments. Cowles Fundation for Research in Economics at Yal University. Monograph 16. Wiley, New York (1959)

    Google Scholar 

  19. Markowitz, H.M.: Mean-Variance Analysis in Portfolio Choice and Capital Markets. Basil Blackwell, Oxford (1987)

    MATH  Google Scholar 

  20. Marszałek, A., Burczyński, T.: Financial fuzzy time series models based on ordered fuzzy numbers. In: Pedrycz, W., Chen, S.-M. (eds.) Time Series Analysis, Model & Applications, ISRL 47, pp. 77–95. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  21. Marszałek, A., Burczyński, T.: Modelling financial high frequency data using ordered fuzzy numbers. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2013. LNCS (LNAI), vol. 7894, pp. 345–352. Springer, Heidelberg (2013). doi:10.1007/978-3-642-38658-9_31

    Chapter  Google Scholar 

  22. Marszałek, A., Burczyński, T.: Modeling and forecasting financial time series with ordered fuzzy candlesticks. Inf. Sci. 273, 144–155 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  23. Murphy, J.J.: Technical Analysis of the Financial Markets. New York Institute of Finance, New York (1999)

    Google Scholar 

  24. Tanaka, H., Guo, P.: Portfolio selection based on upper and lower exponential possibility distributions. Eur. J. Oper. Res. 114, 115–126 (1999)

    Article  MATH  Google Scholar 

  25. Sharpe, W.F.: The sharpe ratio. J. Portfolio Manage. 21(1), 49–58 (1994)

    Article  Google Scholar 

  26. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  MATH  Google Scholar 

  27. Zhang, W.G., Zhang, X.L., Xiao, W.L.: Portfolio selection under possibistic mean-variance utility and SMO algorithm. Eur. J. Oper. Res. 197(2), 693–700 (2009)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Computational Intelligence Department, Institute of Computer Science, Cracow University of Technology, Warszawska 24, 31-155, Cracow, Poland

    Adam Marszałek & Tadeusz Burczyński

  2. Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawinskiego 5B, 02-106, Warsaw, Poland

    Tadeusz Burczyński

Authors
  1. Adam Marszałek
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  2. Tadeusz Burczyński
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Correspondence to Tadeusz Burczyński .

Editor information

Editors and Affiliations

  1. Częstochowa University of Technology, Częstochowa, Poland

    Leszek Rutkowski

  2. Częstochowa University of Technology, Częstochowa, Poland

    Marcin Korytkowski

  3. Częstochowa University of Technology, Częstochowa, Poland

    Rafał Scherer

  4. AGH University of Science and Technology, Kraków, Poland

    Ryszard Tadeusiewicz

  5. University of California, Berkeley, California, USA

    Lotfi A. Zadeh

  6. University of Louisville, Louisville, Kentucky, USA

    Jacek M. Zurada

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Marszałek, A., Burczyński, T. (2017). Fuzzy Portfolio Diversification with Ordered Fuzzy Numbers. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2017. Lecture Notes in Computer Science(), vol 10245. Springer, Cham. https://doi.org/10.1007/978-3-319-59063-9_25

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  • DOI: https://doi.org/10.1007/978-3-319-59063-9_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59062-2

  • Online ISBN: 978-3-319-59063-9

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