Multi-period portfolio selection with dynamic risk/expected-return level under fuzzy random uncertainty

In this study, we discuss multi-period portfolio selection problems when security returns are described as fuzzy random variables. The main concern of this work is to apply dynamic risk tolerance and expected return levels in mathematical modeling; i.e., these two indices of each period are influenced by the investment result of the previous period as well as human risk attitudes instead of static values over the entire investment horizon. Essentially, this assumption is based on the reality that investors tend to update targets when their wealth changes. In addition, fuzzy random variables are employed here to incorporate historical data with expert knowledge when estimating security future returns. Based on the above considerations, two multi-period portfolio selection models are built in light of the different risk attitudes. We then provide property analysis on complicated nonlinear optimization problems and derive several equivalents of the models, which can be solved by the existing dynamic programming. In general situations, a fuzzy random simulation-based particle swarm optimization algorithm is developed to search for approximate optima. The performance of this research is exemplified by a real market data-based case study in which the superiority of the dynamic strategy is demonstrated by a comparison with conventional approaches.