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Fuzzy optimization for portfolio selection based on Embedding Theorem in Fuzzy Normed Linear Spaces

Author

Listed:
  • Solatikia Farnaz

    (Department of Engineering Science, Middle East Technical University, Ankara, Turkey)

  • Kiliç Erdem

    (Department of Economics, MEF University, Istanbul, Turkey)

  • Weber Gerhard Wilhelm

    (Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey)

Abstract

Background: This paper generalizes the results of Embedding problem of Fuzzy Number Space and its extension into a Fuzzy Banach Space C(Ω) × C(Ω), where C(Ω) is the set of all real-valued continuous functions on an open set Ω. Objectives: The main idea behind our approach consists of taking advantage of interplays between fuzzy normed spaces and normed spaces in a way to get an equivalent stochastic program. This helps avoiding pitfalls due to severe oversimplification of the reality. Method: The embedding theorem shows that the set of all fuzzy numbers can be embedded into a Fuzzy Banach space. Inspired by this embedding theorem, we propose a solution concept of fuzzy optimization problem which is obtained by applying the embedding function to the original fuzzy optimization problem. Results: The proposed method is used to extend the classical Mean-Variance portfolio selection model into Mean Variance-Skewness model in fuzzy environment under the criteria on short and long term returns, liquidity and dividends. Conclusion: A fuzzy optimization problem can be transformed into a multiobjective optimization problem which can be solved by using interactive fuzzy decision making procedure. Investor preferences determine the optimal multiobjective solution according to alternative scenarios.

Suggested Citation

  • Solatikia Farnaz & Kiliç Erdem & Weber Gerhard Wilhelm, 2014. "Fuzzy optimization for portfolio selection based on Embedding Theorem in Fuzzy Normed Linear Spaces," Organizacija, Sciendo, vol. 47(2), pages 90-97, May.
    • Handle: RePEc:vrs:organi:v:47:y:2014:i:2:p:8:n:4
    DOI: 10.2478/orga-2014-0010
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