证 券投资组合最优化模型

毕业论文

题目：证券投资组合最优化模型学院：数理学院

专业：数学与应用数学（金融方向）姓名：申圣

学号： 131412135

指导老师：赵许培

完成时间： 2016.5.10

摘要

随着改革开放的进一步加深，中国人民的生活水平进一步的提高，1984年中国发行第一只股票以来中国人民才开始逐步有了投资意识。中国股市用了不到30年的时间走完了西方国家的200年的历史，中国股市虽然发展如此迅速但是伴随着种种问题的出现。投资者理性分析投资市场的少，很多人盲目投资，单单依靠所谓内幕小道的消息等方法已经不能满足对投资的需要，人们渐渐意识到了组合化的投资是未来投资的方向。所以在和数学有关的金融学当中，建立数学模型是研究最优组合投资方法当中的一个很好的策略，数学模型应运而生。

数学模型可以通俗的说成是数学在其他领域当中的应用，所以说证券投资最优化的模型就是在进行股票基金债券进行商业投资过程中所建立的一个使投资收益最大化的数学模型，本文首先简单介绍马柯威茨（markowitz）模型，并且研究了此模型的不足之处，引入偏好系数建立了自己的投资组合最优化数学模型。运用自己所学的《最优化方法》上面的外点罚函数法对此模型进行求解。最后进行实证性分析，得出组合最优化数学模型具有解决实际问题的可行性。

关键词：马柯维茨模型；组合最优化数学模型；共轭梯度；外点惩罚函数；

Abstract

With the further deepening of reform and opening up, Chinese people's living standards further improved, in 1984 China issued the first stock since the Chinese people began to gradually have the consciousness of the investment. China's stock market has taken less than 30 years covered 200 years of history in the west, China's stock market although such rapid development with the advent of the problems. Investors less rational analysis of the investment market, a lot of people blind investment, only rely on methods such as the so-called insider gossip news already cannot satisfy the need for investment, people gradually realized the combination of the investment will be the future direction. So in finance related to mathematics, mathematical model is to study the optimal portfolio investment methods of a good strategy, mathematical model arises at the historic moment.Mathematical model can be popular as the application of mathematics in other areas, so that securities investment optimization model is in stock fund, bond business investment in the process of the established a mathematical model to maximize return on investment, this paper introduces the Ma Kewei, markowitz model, and the deficiency of this model is studied, and the introduction of preference coefficient of his portfolio optimization mathematical model is established. Used his knowledge of the optimization method of above point penalty function method for solving of this model. Through the empirical analysis, the final combination optimization mathematical model with the feasibility of solving practical problems.

Key words:Markowitz model;Combinatorial optimization mathematical model; Conjugate gradient method;Penalty function method;

目录

引言 (1)

1 马柯威茨模型简介 (3)

1.1 数学描述马柯威茨模型 (3)

1.2 组合最优化数学模型 (4)

2 求解组合最优化模型 (6)

2.1 惩罚函数简介 (6)

2.2 运用外点罚函数求解 (6)

2.3 共轭梯度法简介及步骤 (7)

2.4 参考共轭梯度求解模型 (11)

3 实证分析 (14)

致谢 (18)

参考文献 (19)

附录 (20)