Empirical Study Based On Quantum-Behaved Particle Swarm Optimization Stochastic Programming Algorithm

Markowitz advanced his financial portfolio model and also set up the beginning of ration analysis to financial investment. After that, With the rapid development of economy and the deeper research is carried on by the scholars, on the other hand, the circumstance of investment becomes complex and changeful, and demand proposed by the investors becomes higher and higher, so the portfolio optimization model turns to be more complex. As a long-term investor, it is not enough to study the static models. Because the risk is inconsistent with changing of economic environment, the investor should adjust investment strategy and not keep unalterable portfolio until the end time of investment. That is my research: multistage stochastic optimization, which manages portfolio in constantly changing financial markets by periodically rebalancing the asset portfolio to achieve return maximization and risk minimization.The research of portfolio optimization is an uncertain phenomenon. It becomes more and more difficult in resolving it with traditional mathematic programming. However, with the recent development in computers and renovation algorithm, many complex optimization problems can be solved by it. In the world, artificial intelligence methods, such as GA and artificial neural network are introduced to solve the financial portfolio problem while traditional mathematics methods are becoming more and more difficult.In this paper, The Markovitz portfolio model is firstly studied, which is embed into a multistage stochastic optimization model. Then a decision-making process is proposed which is solved by Quantum-behaved Particle Swam Optimization (QPSO) Algorithm, Particle Swam Optimization (PSO), and Genetic Algorithm (GA) to solve multi-stage portfolio optimization problem. In order to evaluate the performance of these three algorithms on multistage financial optimization, experiments were carried out. Weekly closing price of S&P 100 Index and its component stocks from1 January 2000 to 31 December 2005 were collected. The performance of them demonstrated that the PSO converges most rapidly in early stage of the running, but may encounter premature convergence and therefore only find out sub-optima. The GA has the slowest convergence rate than the QPSO and PSO, but it encounters premature convergence less frequently than the PSO. The GA's slow convergence rate may cause the population not to converge to a point in the search space when the running is over. Comparing with the other two algorithms, the QPSO can converge rapidly and search out the global optima most frequently.If the Markowitz portfolio model is set up, a number of covariances need to be evaluated, which need the huge computer capacity to satisfy it. In order to reduce the computational burden, a single index modle is introduced. Then a decision-making process is proposed with the three algorithms. The performance of them demonstrated that QPSO also has a good searching ability.