Intelligent Algorithm Design For The Optimal Portfolio Based On PVaR

With the financial globalization and liberalization,financial organizations made more concentration on risk management in investing operations.Risk measurement as the core element of controlling financial risks becomes the focus in relative study.Period Value at Risk(PVaR)is a recently proposed notation which is suitable for predicting risk level in the later time interval.In the field of portfolio optimization,researchers have established the mixed integer programming(MIP)model to obtain an optimized solution with respect to PVaR value.However,the huge computation effort paid on solving this problem by optimization tool makes it inapplicable in real world practice even if the problem size is small.Based on aforementioned limitations,we try to carry out our research in the following sections:Firstly,we make further investigation on the characteristics of proposed model.Then we utilize the standard particle swarm optimization(standard_PSO)algorithm to solve this problem.Algorithm parameters and comparison are analyzed among algorithms.This standard_PSO can solve the medium scale problems and get a better solution.Secondly,when the scale of the problem or desired return target for investors is larger,the standard_PSO algorithm needs more iteration to find a feasible solution.So we designed the particle swarm algorithm based on grid partitioning initialization strategies(grid_PSO)to improve the standard_PSO algorithm.For small scale problems,this algorithm can locate a high quality solution in a relatively short period of time.For large scale problems,this algorithm was not significantly improved in accuracy of solution.Again,for solving large-scale problems,grid_PSO algorithm was not significantly improved in accuracy of solution.So we designed four strategies incorporated in standard pso to further improve the searching performance regarding to solution quality and computation time.The proposed methods focus on the velocity and position updating formula of each particle.These methods are called meanPbest_PSO algorithm,0.5_PSO algorithm,rand_PSO algorithm and if_PSO algorithm,respectively.Finally,we use statistical t test to analyze the different performance of the standard_PSO algorithm,grid_PSO algorithm,meanPbest_PSO algorithm,0.5_PSO algorithm,rand_PSO algorithm and if_PSO algorithm make some conclusions.