基于改进人工鱼群算法优化投资组合模型的研究

发布时间：2018-01-29 16:35

本文关键词： 人工鱼群投资组合均匀变异 Levy变异优化求解　出处：《天津商业大学》2017年硕士论文　论文类型：学位论文

【摘要】：随着经济的飞速发展,证券投资市场犹如雨后春笋般不断生长,大量的企业和个人对各种证券商品进行投资买卖。在证券市场中,投资本身就会带有一定的风险,有些资产具有高风险,而有些资产具有低风险,投资者必须选择购买哪些证券产品,使得收益更高,这对不同的投资者来说,显得尤为重要。有的投资者具有冒险精神,希望通过高风险的手段获取较高的收益;另外一些不愿意承受如此大的风险,他们更喜欢低风险的投资方式。如何合理选择投资方案,使投资者在可接受的风险范围内获取最高收益,成为目前众多学者研究的热点。自Markowitz首次提出以均值-方差为基础的投资组合问题模型后,许多学者开始采用各种算法对投资组合模型进行优化求解。人工鱼群算法作为一种新兴的优化算法,具有简单、高效和灵活等特点,目前得到广泛应用。但也存在收敛精度不高、易陷入局部极值以及优化求解不够稳定等不足。因此,本文首先对鱼群算法进行改进,然后用于考虑交易费用的投资组合模型的优化求解,获得较好效果。主要工作包括:(1)针对人工鱼群算法的不足,研究了两种改进方式,一种是利用均匀分布产生均匀分布算子,并与基本鱼群算法相结合,当连续若干次收敛最优值变化方差在允许误差之内时发生均匀变异,这样能够保证鱼群跳出局部极值的陷阱,从而获得全局最优状态。另一种是采用服从Levy分布的概率函数使鱼群产生Levy变异,在寻优过程中能够跳出局部极值。经测试函数仿真表明,改进算法提高了收敛精度和全局搜索能力、以及求解问题的稳定性。同时对这两种改进算法还采用自适应视野和步长,进一步提高了算法的收敛性能。(2)在对一般投资组合模型研究的基础上,引入交易费用,讨论了考虑交易费用的投资组合模型。并以上海证券交易所五只股票100天的股票价格数据为实例,分别采用基本鱼群算法、基于自适应视野与步长均匀变异鱼群算法和基于自适应Levy变异人工鱼群算法对投资组合模型进行优化求解。结果表明,改进鱼群算法可以获得较好的投资效益,投资期望收益明显提高、风险降低。
[Abstract]:With the rapid development of economy, the securities investment market is growing like bamboo shoots after a spring rain. A large number of enterprises and individuals invest in various securities commodities. Investment itself will have a certain risk, some assets have high risk, while some assets have low risk, investors must choose which securities products to buy to make the return higher, this is for different investors. Some investors have the spirit of taking risks and hope to obtain higher returns by means of high risk; Others are not willing to take such a large risk, they prefer low-risk investment. How to choose a reasonable investment plan, so that investors can get the highest return within the acceptable risk range. Since Markowitz first proposed a portfolio problem model based on mean-variance. Many scholars began to use a variety of algorithms to optimize the portfolio model. Artificial fish swarm algorithm as a new optimization algorithm, with the characteristics of simple, efficient and flexible. At present, it is widely used. However, it also has some shortcomings such as low convergence precision, easy to fall into local extremum and unstable optimization. Therefore, this paper first improves the fish swarm algorithm. Then the optimal solution of portfolio model considering transaction cost is used to obtain better results. The main work includes: 1) aiming at the shortcomings of artificial fish swarm algorithm, two improved methods are studied. One is to use uniform distribution to generate uniform distribution operator, and combine with the basic fish swarm algorithm, when the variance of the optimal value of convergence is within the allowable error, the uniform variation occurs. In this way, the fish group can escape from the trap of local extremum and obtain the global optimal state. The other is to use the probability function of Levy distribution to make the fish herd produce Levy variation. It can jump out of the local extremum in the process of optimization. The test function simulation shows that the improved algorithm improves the convergence accuracy and global search ability. And the stability of solving the problem. At the same time, the adaptive field of vision and step size are also used to improve the convergence performance of the algorithm. 2) on the basis of the general portfolio model research. This paper introduces the transaction cost and discusses the portfolio model considering the transaction cost. Taking the 100-day stock price data of five stocks on the Shanghai Stock Exchange as an example, the basic fish swarm algorithm is adopted respectively. Based on adaptive visual field and step size uniform mutation fish swarm algorithm and adaptive Levy mutation artificial fish swarm algorithm to optimize the solution of the portfolio model. The improved fish swarm algorithm can obtain better investment benefit, the expected return of investment is obviously increased, and the risk is reduced.
【学位授予单位】：天津商业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F832.51

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