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

Solatikia Farnaz (), Erdem Kilic and Weber Gerhard Wilhelm ()
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Solatikia Farnaz: Department of Engineering Science, Middle East Technical University, Ankara, Turkey
Weber Gerhard Wilhelm: Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey

Organizacija, 2014, vol. 47, issue 2, 90-97

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.

Keywords: Embedding problem; Fuzzy optimization; Fuzzy Banach Space; Portfolio selection (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:vrs:organi:v:47:y:2014:i:2:p:8:n:4

DOI: 10.2478/orga-2014-0010

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