Fuzzy multi-objective portfolio model based on semi-variance–semi-absolute deviation risk measures

The risk measure plays an important role for portfolio selection problem. The lower partial risk (downside risk) measures have been considered to be more in line with investor’s attitude toward risk. The purpose of this paper is to construct a portfolio selection model in the lower partial risk framework. First, semi-variance and semi-absolute deviation risk measures are used as double-risk measures simultaneously, which can overcome the shortcomings of both semi-variance risk measure and semi-absolute deviation risk measure and can provide additional strengths and flexibility. Second, to address a real portfolio selection problem, by considering the transaction cost and liquidity of portfolio, and regarding the returns of risk assets as LR-type fuzzy variables, we present a fuzzy multi-objective portfolio selection model. Third, in order to limit the proportion of the portfolio invested in assets with common characteristics and to avoid very small holdings, the quantity and class constraints are introduced into the model. Finally, to solve the proposed model efficiently, a new multi-objective evolutionary algorithm is designed. Furthermore, some experiments are conducted by using the data of Shanghai Stock Exchange, and the results indicate the efficiency and effectiveness of the proposed model and algorithm.