Portfolio selection models with technical analysis-based fuzzy birandom variables

Recently, fuzzy set theory has been widely employed in building portfolio selection models where uncertainty plays a role. In these models, future security returns are generally taken for fuzzy variables and mathematical models are then built to maximize the investment profit according to a given risk level or to minimize a risk level based on a fixed profit level. Based on existing works, this paper proposes a portfolio selection model based on fuzzy birandom variables. Two original contributions are provided by the study: First, the concept of technical analysis is combined with fuzzy set theory to use the security returns as fuzzy birandom variables. Second, the fuzzy birandom Value-at-Risk (VaR) is used to build our model, which is called the fuzzy birandom VaR-based portfolio selection model (FBVaR-PSM). The VaR can directly reflect the largest loss of a selected case at a given confidence level and it is more sensitive than other models and more acceptable for general investors than conventional risk measurements. To solve the FBVaR-PSM, in some special cases when the security returns are taken for trapezoidal, triangular or Gaussian fuzzy birandom variables, several crisp equivalent models of the FBVaR-PSM are derived, which can be handled by any linear programming solver. In general, the fuzzy birandom simulation-based particle swarm optimization algorithm (FBS-PSO) is designed to find the approximate optimal solution. To illustrate the proposed model and the behavior of the FBS-PSO, two numerical examples are introduced based on investors' different risk attitudes. Finally, we analyze the experimental results and provide a discussion of some existing approaches.