Formulation of the Non-Parametric Value at Risk Portfolio Selection Problem Considering Symmetry.

In this research, we study the non-parametric portfolio selection problem with Value at Risk (VaR) minimization and establish a new enhanced Mixed Integer Linear Programming (MILP) formulation to obtain the optimal solutions considering the symmetric property of VaR. We identify that the new MILP formulation can significantly reduce the computation burden of the MILP solver CPLEX. To solve larger-scale practical portfolio selection problems in reasonable computation time, we also develop the Particle Swarm Optimization (PSO) algorithm integrating an efficient Fast Feasible Solution Detection (FFSD) scheme to obtain the near-optimal solutions. Using the simulated datasets with different distribution parameters and skewness and kurtosis patterns, some preliminary numerical results are provided to show the efficiency of the new formulation and FFSD scheme.