Advertisement

Robust Portfolio Selection Model with Random Fuzzy Returns Based on Arbitrage Pricing Theory and Fuzzy Reasoning Method

  • Takashi Hasuike
  • Hideki Katagiri
  • Hiroshi Tsuda
Chapter
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 186)

Abstract

This paper considers a robust-based random fuzzy mean-variance portfolio selection problem using a fuzzy reasoning method, particularly a single input type fuzzy reasoning method. Arbitrage Pricing Theory (APT) is introduced as a future return of each security, and each factor in APT is assumed to be a random fuzzy variable whose mean is derived from a fuzzy reasoning method. Furthermore, under interval inputs of fuzzy reasoning method, a robust programming approach is introduced in order to minimize the worst case of the total variance. The proposed model is equivalently transformed into the deterministic nonlinear programming problem, and so the solution steps to obtain the exact optimal portfolio are developed.

Keywords

Portfolio selection problem Arbitrage pricing theory (APT) Random fuzzy programming Fuzzy reasoning method Robust programming Equivalent transformation Exact solution algorithm 

References

  1. 1.
    Elton EJ, Gruber MJ (1995) Modern portfolio theory and investment analysis. Wiley, New YorkGoogle Scholar
  2. 2.
    Goldfarb D, Iyengar G (2003) Robust portfolio selection problems. Math Operat Res 28:1–38MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Hasuike T, Katagiri H, Ishii H (2009) Multiobjective random fuzzy linear programming problems based on the possibility maximization model. J Adv Comput Intell Intellt Inform 13(4):373–379Google Scholar
  4. 4.
    Hasuike T, Katagiri H, Ishii H (2009) Portfolio selection problems with random fuzzy variable returns. Fuzzy Sets Syst 160:2579–2596MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Hasuike T, Katagiri H, Tsuda H (2012) Robust-based random fuzzy mean-variance model using a fuzzy reasoning method. In: Lecture notes in engineering and computer science: proceedings of the international multi conference of engineers and computer scientists 2012, IMECS 2012, 14–16 March, 2012, Hong Kong, pp 1461–1466Google Scholar
  6. 6.
    Hayashi K, Otsubo A, Shiranita K (1999) Realization of nonlinear and linear PID control using simplified direct inference method. IEICE Trans Fundam (Japanese Edition), J82-A(7), pp 1180–1184Google Scholar
  7. 7.
    Hayashi K, Otsubo A, Shirahata K (2001) Improvement of conventional method of PI fuzzy control. IEICE Trans Fundam E84-A(6), pp 1588–1592Google Scholar
  8. 8.
    Huang X (2007) Two new models for portfolio selection with stochastic returns taking fuzzy information. Eur J Oper Res 180:396–405MATHCrossRefGoogle Scholar
  9. 9.
    Inuiguchi M, Ramik J (2000) Possibilisitc linear programming: A brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem. Fuzzy Sets Syst 111:3–28MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Katagiri H, Hasuike T, Ishii H, Nishizaki I (2008) Random fuzzy programming models based on possibilistic programming. In:Proceedings of the 2008 IEEE international conference on systems, man and cybernetics (to appear)Google Scholar
  11. 11.
    Katagiri H, Ishii H, Sakawa M (2004) On fuzzy random linear knapsack problems. CEJOR 12:59–70MathSciNetMATHGoogle Scholar
  12. 12.
    Katagiri H, Sakawa M, Ishii H (2005) A study on fuzzy random portfolio selection problems using possibility and necessity measures. Scientiae Mathematicae Japonocae 65:361–369MathSciNetGoogle Scholar
  13. 13.
    Konno H, Yamazaki H (1991) Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Manage Sci 37:519–531CrossRefGoogle Scholar
  14. 14.
    Konno H, Shirakawa H, Yamazaki H (1993) A mean-absolute deviation-skewness portfolio optimization model. Ann Oper Res 45:205–220MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Leon RT, Liern V, Vercher E (2002) Validity of infeasible portfolio selection problems: fuzzy approach. Eur J Oper Res 139:178–189MATHCrossRefGoogle Scholar
  16. 16.
    Lintner BJ (1965) Valuation of risky assets and the selection of risky investments in stock portfolios and capital budgets. Rev Econ Stat 47:13–37CrossRefGoogle Scholar
  17. 17.
    Liu B (2002) Theory and practice of uncertain programming. Physica Verlag, HeidelbergGoogle Scholar
  18. 18.
    Lobo MS (2000) Robust and convex optimization with applications in finance. Doctor thesis of the department of Electrical engineering and the committee on graduate studies, Stanford University, StanfordGoogle Scholar
  19. 19.
    Luenberger DG (1997) Investment science, Oxford University Press, OxfordGoogle Scholar
  20. 20.
    Markowitz HM (1952) Portfolio selection. J Financ 7(1):77–91Google Scholar
  21. 21.
    Mamdani EH (1974) Application of fuzzy algorithms for control of simple dynamic plant. Proc IEE 121(12):1585–1588Google Scholar
  22. 22.
    Mossin J (1966) Equilibrium in capital asset markets. Econometrica 34(4):768–783CrossRefGoogle Scholar
  23. 23.
    Rockafellar RT, Uryasev S (2000) Optimization of conditional value-at-risk. J Risk 2(3):1–21Google Scholar
  24. 24.
    Ross S (1976) The arbitrage theory of capital asset pricing. J Econ Theory 13(3):341–360CrossRefGoogle Scholar
  25. 25.
    Sharpe WF (1964) Capital asset prices: A theory of market equivalent under conditions of risk. J Financ 19(3):425–442MathSciNetGoogle Scholar
  26. 26.
    Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst Man Cybern SMC-15(1), pp 116–132Google Scholar
  27. 27.
    Tanaka H, Guo P (1999) Portfolio selection based on upper and lower exponential possibility distributions. Eur J Oper Res 114:115–126MATHCrossRefGoogle Scholar
  28. 28.
    Tanaka H, Guo P, Turksen IB (2000) Portfolio selection based on fuzzy probabilities and possibility distributions. Fuzzy Sets Syst 111:387–397MathSciNetMATHCrossRefGoogle Scholar
  29. 29.
    Vercher E, Bermúdez JD, Segura JV (2007) Fuzzy portfolio optimization under downside risk measures. Fuzzy Sets Syst 158:769–782MATHCrossRefGoogle Scholar
  30. 30.
    Watada J (1997) Fuzzy portfolio selection and its applications to decision making. Tatra Mountains Math Pub 13:219–248MathSciNetMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Takashi Hasuike
    • 1
  • Hideki Katagiri
    • 2
  • Hiroshi Tsuda
    • 3
  1. 1.Graduate School of Information Science and TechnologyOsaka UniversitySuitaJapan
  2. 2.Graduate School of EngineeringHiroshima UniversityHigashi-HiroshimaJapan
  3. 3.Department of Mathematical Sciences, Faculty of Science and EngineeringDoshisha UniversityKyotanabeJapan

Personalised recommendations