Research Of Portfolio Optimization Model Based On Improved Artificial Fish Swarm Algorithm

With the rapid development of the economy,the stock market is growing like mushrooms,and a large number of enterprises and individuals invest in all kinds of securities.In the stock market,the investment itself with a certain risk,some assets have high risk,and some assets with low risk,investors must choose which securities products to makes higher income,it is particularly important for different investors.Some investors have the spirit of adventure,and hope to get a higher income by means of high risk;others do not want to take such a big risk,they prefer low-risk investment.How to choose the investment plan reasonably so that investors can get the highest return on acceptable risk level,which has become the focus of many scholars.Since Markowitz first proposed the mean variance based portfolio model,many scholars begin to use various algorithms to optimize the portfolio model.As a new optimization algorithm,artificial fish swarm algorithm is simple,efficient and flexible,which has been widely used currently.But there are some shortcomings,such as low convergence accuracy,easy to fall into local extremum,and the stability of the optimization problem is not stable enough.Therefore,this paper firstly improves the fish swarm algorithm,then which is used to optimizing the solution of the portfolio model with transaction costs,so that achieve better results.Main tasks include:(1)Aiming at the shortage of artificial fish swarm algorithm,two improved methods are studied.One is use uniform distribution to generate uniform distribution operators,which is combined with the basic fish swarm algorithm.Uniform variation occurs when the variance of the optimal value of the successive convergence is within the allowable error.In this way,the trap of the fish out of the local extremum can be guaranteed so as to obtain the global optimum.The other is use a probability function obeying the Levy distribution to make Levy variations in fish swarm.In the process of optimization,fish swarm could jump out of local extremes.The test function simulation shows that the improved algorithm improves the convergence accuracy and global search ability,and solves the stability of the problem.At the same time,adaptive vision and step size are adopted to improve the convergence performance of the two improved algorithms.(2)On the basis of the study of the general portfolio model,the transaction cost is introduced,and the portfolio model with transaction costs is discussed.And this paper take the stock exchange price data of five stocks in Shanghai stock exchange for 100 days as an example.Using the basic fish swarm algorithm,the adaptive visual field and the step length uniform variation fish swarm algorithm and the adaptive Levy mutation artificial fish swarm algorithm to optimize the portfolio model respectively.The results show that the improved fish swarm algorithm can achieve better investment efficiency,which increase the expected return of investment and reduce the risk meanwhile.