A fuzzy mean semi-absolute deviation-semi-variance-proportional entropy portfolio selection model with transaction costs

Abstract

In recent years, the downside risk measure is considered to be more in line with investors’ attitudes towards risk. The purpose of this paper is to establish a diversified portfolio selection model under the downside risk framework. Firstly, a fuzzy mean semi-absolute deviation-semi-variance-proportional entropy portfolio selection model with transaction costs is proposed, based on Markowitz’s mean-variance model, in which semi-absolute deviation and semi-variance are taken as the risk measure. That is to say, the possibilistic mean of the investment rate of return is used to quantify the return of the portfolio, and the possibilistic semi-absolute deviation and possibilistic semi-variance are used to measure investment risk. The shortcomings of semi-absolute deviation or semi-variance as a risk measure individually can be overcome when the semi-absolute deviation is combined with semi-variance as a dual risk measure. Meanwhile, a proportional entropy function based on the Minkowski measure is used to construct the proposed model to diversify the portfolio. Secondly, a new multi-objective bat algorithm is designed to solve the model, and the experiments were conducted by using data from the Shanghai Stock Exchange to prove the effectiveness of the model.