Dynamic multi-period sparse portfolio selection model with asymmetric investors’ sentiments

• The asymmetric investors’ sentiments are taken into account in the dynamic portfolio. • Investors’ behavior related investment decisions are modelled by Prospect Theory. • Dynamic iteration rule of the investor’s expected return level is introduced. • Sparse solutions of the presented model are given by the re-parametrisation algorithm. • The terminal return is enhanced 9% and terminal risk is reduced 11.75%. Asymmetric investors’ sentiments on returns and risks play an important role in updating the portfolio strategies in multi-period portfolio selection problems. By introducing the Prospect Theory to measure the asymmetric investors’ sentiments, a dynamic sentiment-adjusted model (DSAM) is proposed to sparse portfolio selection problem over multiple periods, in which the objective is to minimize the risk of the portfolio. As we focus on the sparse portfolio, a l 0 constraint is added to our model. The l 0 constraint represents that we can only purchase at most k securities from N candidate securities, in which k is a small number compared to N . Since the objective function of the sparse portfolio with l 0 constraint is NP-hard, and could not be solved by the Deep Learning algorithms. The stochastic neural networks algorithm with re-parametrisation trick (SNNrP) is introduced to solve the DSAM. The back-testing framework of our paper includes a multi-period portfolio selection model, in which asymmetric investors’ sentiments are modeled to iterate investors’ expected return level each period. In the back-testing framework, we conduct the experiments for different investment periods with different investors’ sentiments. The experimental results for the Nasdaq and CSI 300 data sets show that, on average, compared with the traditional Mean–variance model, the terminal return and risk obtained by the DSAM model outperforms by 9% and 11.75%.