A Fuzzy Portfolio Model With Cardinality Constraints Based on Differential Evolution Algorithms

A Fuzzy Portfolio Model With Cardinality Constraints Based on Differential Evolution Algorithms

JianDong He
Copyright: © 2024 |Pages: 14
DOI: 10.4018/IJDWM.341268
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Abstract

Uncertain information in the securities market exhibits fuzziness. In this article, expected returns and liquidity are considered as trapezoidal fuzzy numbers. The possibility mean and mean absolute deviation of expected returns represent the returns and risks of securities assets, while the possibility mean of expected turnover represents the liquidity of securities assets. Taking into account practical constraints such as cardinality and transaction costs, this article establishes a fuzzy portfolio model with cardinality constraints and solves it using the differential evolution algorithm. Finally, using fuzzy c-means clustering algorithm, 12 stocks are selected as empirical samples to provide numerical calculation examples. At the same time, fuzzy c-means clustering algorithm is used to cluster the stock yield data and analyse the stock data comprehensively and accurately, which provides a reference for establishing an effective portfolio.
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Preliminary Knowledge

In the fuzzy set theory, to describe the possibility of a fuzzy event occurring, Zedeh put forward the theory of possibility (Zadeh,1965), which is considered as a critical moment during which the fuzzy set theory experienced the development. Along with the development of the fuzzy set theory, a variety of phenomena of fuzzy uncertainties in the financial market is increasingly attracting the attention of a great number of scholars. Therefore, considerable studies conducted by these scholars employ the fuzzy set theory to address these phenomena of uncertainties that exist in the financial market. It is found that the fuzzy set theory is a powerful analytic tool in studying these phenomena of uncertainties in the stock. Today, the fuzzy portfolio has become a common research focus.

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