含交易费用的实用型资产分配优化模型研究

发布时间：2018-03-08 09:35

本文选题：Markowitz模型　切入点：风险规避参数　出处：《广东工业大学》2017年硕士论文　论文类型：学位论文

【摘要】：近年来股票交易市场持续火热,如此良好的投资背景下,如何有效地规避风险,构建合理科学的投资组合优化模型是目前迫切需要解决的问题,受到政府以及广大国内外学者的关注和研究.目前投资组合优化模型有马科维茨(Markowitz)的均值方差模型、资本资产定价模型、套利定价理论(apt)等,并针对各种模型研究了多种求解算法.从近来A股市场的分析来看,马科维茨理论对于大型基金和资产管理有一定的应用价值.然而实际股票市场进行交易都是在证券公司这个平台上进行的,所以交易费用在实际的证券交易中所占比重还是不能忽略的[1],也就是说运用马科维茨理论的一个重要预设——不存在交易费用,在解决证券交易市场投资组合问题就不适用了.本文在马科维茨经典理论的基础上,针对它预设条件的弊端,建立了改进后的更实用的资产分配优化模型,并引入投资实例,用分区域多目标进化算法进行求解.文章的具体工作为:首先引入风险规避参数,提出了改进的Markowitz模型,确立了两个优化目标,即收益最大化和风险最小化的多目标优化问题模型.在对证券交易市场交易费用征收规定进行深入研究后,以1手(100股)为单位,构建了交易费用函数并将它引入到改进的Markowitz模型中,并结合实例,用各种函数和excel工具对证券数据进行处理,并用分区域多目标进化算法对其进行求解,得到了较为满意的数值解.其次研究了加入无风险证券的含交易费用的实用型资产分配优化模型,改进了相应的约束条件,通过设定参数值,用分区域多目标进化算法编程求解,得到了和理论情形较为符合的投资结果.最后研究了在约束条件中加入0-1随机变量的基数约束的含交易费用的实用型资产分配优化模型,并对投资比例上下界进行分离限制,从而灵活约定投资项目数目,通过模型仿真,验证了此模型的设计初衷——均衡了投资的收益和风险.
[Abstract]:In recent years, the stock market continues to be hot, so under such a good investment background, how to effectively avoid risks and build a reasonable and scientific portfolio optimization model is an urgent problem to be solved at present. The current portfolio optimization models include Markowitz Markowitz's mean variance model, capital asset pricing model, arbitrage pricing theory and so on. From the recent analysis of the A-share market, we have studied a variety of algorithms for solving various models. Markowitz's theory has some application value for large funds and asset management. However, the actual stock market trading is carried out on the platform of securities companies. Therefore, the proportion of transaction costs in actual securities trading can not be ignored [1], that is to say, using an important presupposition of Markowitz's theory, there is no transaction cost. On the basis of Markowitz's classical theory, a more practical optimization model of asset allocation is established based on Markowitz's classical theory, and an investment example is introduced. The specific work of this paper is as follows: firstly, the risk aversion parameter is introduced, an improved Markowitz model is proposed, and two optimization objectives are established. That is, the multi-objective optimization problem model of maximization of income and minimization of risk. The transaction cost function is constructed and introduced into the improved Markowitz model. Combined with an example, various functions and excel tools are used to process the securities data, and the multi-objective evolutionary algorithm is used to solve the problem. A more satisfactory numerical solution is obtained. Secondly, the practical asset allocation optimization model with transaction costs is studied, and the corresponding constraint conditions are improved. The multi-objective evolutionary algorithm is used to solve the problem, and the investment results are obtained, which are in good agreement with the theoretical results. Finally, a practical asset allocation optimization model with transaction costs is studied, in which the cardinality constraints of 0-1 random variables are added to the constraints. The investment ratio is restricted by the separation of the upper and lower bounds, and the number of investment projects is flexibly agreed. Through the simulation of the model, it is verified that the original intention of the model is to balance the income and risk of the investment.
【学位授予单位】：广东工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F830.91;F224

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