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Fuzzy optimization for portfolio selection based on Embedding Theorem in Fuzzy Normed Linear Spaces
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[15811832 - Organizacija] Fuzzy optimization for portfolio selection based on Embedding Theorem in Fuzzy Normed Linear Spaces.pdf
Date
2014-5-1
Author
Solatikia, Farnaz
Kiliç, Erdem
Weber, Gerhard Wilhelm
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Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
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<jats:title>Abstract</jats:title> <jats:p>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. </jats:p> <jats:p>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. </jats:p> <jats:p>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. </jats:p> <jats:p>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. </jats:p> <jats:p>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.</jats:p>
Subject Keywords
Embedding problem
,
Fuzzy optimization
,
Fuzzy Banach Space
,
Portfolio selection
URI
https://hdl.handle.net/11511/51456
Journal
Organizacija
DOI
https://doi.org/10.2478/orga-2014-0010
Collections
Graduate School of Applied Mathematics, Article
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F. Solatikia, E. Kiliç, and G. W. Weber, “Fuzzy optimization for portfolio selection based on Embedding Theorem in Fuzzy Normed Linear Spaces,”
Organizacija
, pp. 90–97, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/51456.