Abstract
In this paper, we study the portfolio selection problem considering transaction costs under multiple periods. For non-professional investors, it is a critical factor to choose an appropriate model among multiple portfolio selection models in investment. Based on the credibility measure, we formulate a multi-period polynomial portfolio selection model to gather the risk indicators involving variance, semi-variance, entropy, and semi-entropy, helping investors bet on assets. According to the polynomial goal programming (PGP) approach, investors can conquer the fields by combining apposite indicators to build appropriate models. Subsequently, an adjusted genetic algorithm on the foundation of the penalty function is designed to obtain the optimal solution of this multi-period model. The results indicate that the PGP method is suitable for investors to choose the model and assigns the proper models to investors with different risk preferences.
Highlights
Portfolio selection theory is an important part of modern quantitative finance
After this brief Introduction, this paper introduces the conceptions of credibility theory, i.e., credibilistic expectation, variance, semi-variance, entropy, and semi-entropy, in Section 2; based on the PGP method, a multi-period polynomial goal programming model is presented in Section 3, which considers transaction costs, upper and lower bounds, investment proportion, and short-sale to a large extent; in Section 4, the defuzzification portfolio selection model is solved by an adjusted genetic algorithm; followed by Sections 5 and 6, providing an empirical application to demonstrate the results of the comparison of models and the final conclusion, respectively
We investigated the performance of different risk indicators in a multi-period polynomial portfolio selection problem considering transaction costs based on the credibility measure
Summary
Portfolio selection theory is an important part of modern quantitative finance. Generally, investors allocate the funds among different assets to maximize expected returns by choosing an optimal investment strategy, which is known as the portfolio selection problem. Used entropy as a measure of risk and proposed two credibility-based fuzzy mean-entropy models to illustrate the effect of entropy in portfolios. Within the framework of credibility theory, Guo et al [20] designed a fuzzy simulation-based genetic algorithm to settle the fuzzy multi-period mean-variance model involving V-shaped transaction costs. Formulated a bi-objective mean-VaR portfolio selection model with multiple periods and transaction cost considerations based on credibility theory and adopted an interactive dynamic programming method to solve this model. In order to study the extent to which these indicators affect the model, a portfolio selection model is proposed from the perspective of studying different risk indicators and their impacts in a multi-period multi-objective portfolio selection problem under the fuzzy environment. From the perspective of empirical data, the priorities to which investors with different risk preferences prefer different risk indicators or portfolio selection models involving different combination of risk indicators are given, helping investors make more rational decisions
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