证券组合投资决策的均匀试验设计优化研究

发布时间：2018-02-15 11:29

本文关键词： 组合投资决策稳定分布配方均匀设计数据包络分析　出处：《青岛大学》2012年硕士论文　论文类型：学位论文

【摘要】：试验设计是数理统计中的一个重要的分支,是关于试验与分析的统计理论,是进行科学研究的重要工具。各种试验设计与数据处理方法,是以概率论、数理统计等数学理论知识为基础的。本文介绍了均匀设计的理论以及配方均匀设计在证券组合投资决策中的应用。“均匀设计”比其他试验设计方法更适合于多水平数的试验设计,它不但能减少试验的次数,而且能保证试验点均匀地分散在整个试验范围内。经过30多年的推广和发展,均匀设计法已经被广泛地应用于化工、医药、电子、生物、军事工程、食品、社会经济等诸多领域,并取得了显著的经济和社会效益。随着中国经济的飞速发展,居民的收入水平有了显著的提高,可支配收入在收入中的比重越来越大,人们的理财观念也越来越强。为了获得经济收益,人们将剩余收入投入到证券市场中,而为了分散风险,人们构建投资组合进行分散化投资。这就需要投资者具有良好的投资决策和投资方法,尽可能地将投资失误减少到最低。应用最广泛的是马柯维茨的均值-方差模型,但是它的一个前提是假设证券市场的收益率服从正态分布。本文针对证券收益率具有的“高峰厚尾”现象,提出了基于稳定分布的组合投资模型,应用配方均匀设计工具给出组合投资问题的试验设计方法,并用数据包络分析方法对各个组合投资方案的效率进行评价,给出最优的投资决策。最后通过实例验证了模型的可行性。均匀设计作为一种重要的试验设计方法,是我国独创的。将试验设计运用于我国证券市场组合投资的决策中,不必假设证券市场的收益率服从于正态分布,这不仅更适合于证券市场的实际,还能够更好地指导投资者进行投资,不但具有一定的理论价值,而且具有重要的现实意义。
[Abstract]:Experimental design is an important branch of mathematical statistics. It is a statistical theory about experiment and analysis, and an important tool for scientific research. All kinds of experimental design and data processing methods are based on probability theory. This paper introduces the theory of uniform design and the application of formula uniform design in portfolio investment decision. "uniform design" is more suitable for multi-water than other experimental design methods. The experimental design of the flat number, The uniform design method has been widely used in chemical, pharmaceutical, electronic, biological and military engineering after more than 30 years of promotion and development. Food, social and economic fields, and achieved significant economic and social benefits. With the rapid development of China's economy, the income level of residents has been significantly improved, the proportion of disposable income in income is increasing, and people's financial management concept is becoming stronger and stronger. People put the rest of their income into the securities market, and in order to diversify risk, people build portfolios to diversify their investments, which requires that investors have good investment decisions and methods. Minimize investment errors as far as possible. The most widely used is Markowitz's mean-variance model. But one of its presuppositions is that the return rate of the securities market is assumed to follow the normal distribution. In this paper, a portfolio investment model based on stable distribution is proposed in view of the "peak and thick tail" phenomenon of the security yield. The experimental design method of portfolio investment problem is given by using the formula uniform design tool, and the efficiency of each portfolio investment scheme is evaluated by data envelopment analysis method. The optimal investment decision is given. Finally, the feasibility of the model is verified by an example. As an important experimental design method, uniform design is original in our country. It is not necessary to assume that the return rate of the securities market follows the normal distribution when the experimental design is applied to the portfolio investment decision of our country's securities market. This is not only more suitable for the reality of the securities market, but also a better guide for investors to invest, which not only has certain theoretical value, but also has important practical significance.
【学位授予单位】：青岛大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F832.51;F224

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