遗传算法在证券投资中的应用研究

发布时间：2018-03-04 14:20

本文选题：双层遗传算法　切入点：投资组合　出处：《河北工业大学》2014年硕士论文　论文类型：学位论文

【摘要】：证券投资具有市场变化快、影响因素复杂、风险不确定性等特点。为了分散风险，，需按照不同的比例选择多个不同的证券进行投资，即采用投资组合的方式。投资组合问题属于复杂的优化问题，常规的算法难以在短时间内找到全局最优解，而遗传算法的普适性强、对目标函数的性质几乎没要求等特点，为投资组合问题的求解找到了可行的方法。本文主要探讨了如何建立投资组合模型，研究了如何根据具体问题设计模型求解的算法。本文综合经济学理论中的效用论和理性人假设以及统计学理论中的组合方差公式，依据CAPM模型和夏普比率中衡量风险的方法，提出了一个全新的证券投资组合模型：基于单位系统性风险的超额收益模型。该模型以组合标准差衡量风险，以单位系统性风险下的超额收益最大化为目标函数，根据单位风险收益来比较不同投资组合的优劣。建立在单位风险基础上的收益最大化模型，相对于单纯追求收益最大化的模型综合考虑了风险的因素，更符合现实中的投资需求。文章在详细给出了模型的推导过程之后，为模型设计了遗传算法求解。本文独创性的设计了双层遗传算法来解决证券投资组合问题。第一层遗传算法使用财务比率编码，持有期收益率作为适应函数，其运算结果筛选出了供模型使用的样本范围。第二层遗传算法针对模型详细设计了权重编码，直接使用模型的目标函数作为适应函数，对投资组合模型进行求解，使最终结果能够确定出一个组合各证券的投资比例。本文最后以沪深A股市场为例，运用实证分析实现了算法，验证了使用该模型进行投资可以有效的分散风险，选出的证券按比例进行投资其持有期收益率高于市场平均水平，模型和算法取得了较好的结果。
[Abstract]:Securities investment has the characteristics of fast market change, complex influencing factors and uncertainty of risk. In order to disperse risk, it is necessary to select multiple different securities to invest according to different proportions. That is to say, the portfolio problem is a complex optimization problem, and the conventional algorithm is difficult to find the global optimal solution in a short time. However, the genetic algorithm has the characteristics of strong universality and little requirement for the properties of the objective function. This paper mainly discusses how to establish the portfolio model and how to design the algorithm of solving the model according to the specific problem. This paper synthesizes the utility theory and rational man hypothesis in economic theory and the combination variance formula in statistical theory, according to the CAPM model and the method of measuring risk in Sharp ratio. This paper presents a new portfolio model: excess return model based on unit systemic risk, which measures the risk based on the standard deviation of the portfolio, and takes the maximization of the excess return under the unit systemic risk as the objective function. This paper compares the advantages and disadvantages of different investment portfolios according to the unit risk return. The profit maximization model based on the unit risk considers the risk factors compared with the model which simply pursues the income maximization. After giving the derivation process of the model in detail, a genetic algorithm is designed for solving the model. In this paper, a two-layer genetic algorithm is designed to solve the portfolio problem. The second layer genetic algorithm designs the weight coding for the model in detail, and directly uses the objective function of the model as the fitness function to solve the portfolio model. Enables the final result to determine the investment ratio of a portfolio of securities. Finally, taking the Shanghai and Shenzhen A share market as an example, we use the empirical analysis to realize the algorithm, and verify that using this model to invest can effectively spread the risk, and select the securities to invest in a proportionate rate of return higher than the market average. The model and algorithm obtained good results.
【学位授予单位】：河北工业大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TP18;F830.91;F224

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