有限维向量空间中线性定价函数的特征及应用.doc
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有限维向量空间中线性定价函数的特征及应用,19000多字 摘要 通过构建金融学中未定权益空间与线性空间间的对应关系，利用线性空间的性质特征等研究满足一价定律的金融市场等价于线性定价法则之事实，研究有价证券（债券、股票等）的无套利资产定价问题。 考虑到现有的线性定价法则大都较为抽象，难以为初学者理解和应用，正是基于这一问题...
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有限维向量空间中线性定价函数的特征及应用
19000多字
摘要 通过构建金融学中未定权益空间与线性空间间的对应关系，利用线性空间的性质特征等研究满足一价定律的金融市场等价于线性定价法则之事实，研究有价证券（债券、股票等）的无套利资产定价问题。
考虑到现有的线性定价法则大都较为抽象，难以为初学者理解和应用，正是基于这一问题的考量，本文拟透过探究有限维向量空间上线性定价函数的基本特征，提出并研究了基于黄金分割法下的线性定价函数，同时给出了其相应的应用研究。
首先，由金融学中的线性定价法则及数学中的黄金分割率给出了黄金分割线性定价法的定义；其次，简单介绍其一些性质；最后，给出了基于黄金分割法的国债及股票的实证分析。
实证结果表明：本文给出的黄金分割线性定价法对于债券、股票等有价证券买卖时点选择的研究结论是有效、合理的，具有一定的理论和实际意义。
关键词: 未定权益空间 线性定价函数 黄金分割线性定价法
Characteristics and application of linear pricing functions in finite dimensional vector space
Abstract By building in finance contingent claim corresponding relationship between space and linear space, by using the properties of linear space characteristics research meet the law of one price the fact of the financial markets is equivalent to the linear pricing law, the securities (bonds, stocks, etc.) no arbitrage asset pricing problem.
Considering the existing linear pricing rules are rather abstract, difficult to understand for beginners and applications, it is based on the consideration of the problem, this paper intends to explore the finite dimensional vector space through on the basic characteristics of the linear pricing function, put forward and studied based on the linear pricing function under the golden section method, and presents the corresponding application research.
First of all, by the finance of the golden ratio in linear pricing principle and mathematical definition of golden mean linear pricing is presented; Secondly, the simple introduction to some of its properties; Finally, based on the golden section method is given and the empirical analysis of the stock of public debt.
The empirical results show that: in this paper the golden linear pricing for bonds, stocks and other securities trading point selected research conclusion is reasonable and effective, has a certain theoretical and practical significance.
Keywords Contingent claims space The linear pricing function The golden section linear pricing
目 次
1 引言 1
1.1 选题的背景 1
1.2 研究现状 1
1.3 本文的创新点 2
2 金融学中的基本数学知识 4
2.1 有限维线性空间 4
2.2 有限维未定权益空间的完全市场和不完全市场 6
2.3 有限维未定权益空间上的线性定价法 9
2.4 线性定价函数的特征 15
3 有限维向量空间上黄金分割线性定价函数及其应用 17
3.1 定价之黄金分割法 17
3.2 黄金分割线性定价法则应用 18
3.2.1 黄金分割线性定价之国债买卖选择时点计量 18
3.2.2 黄金分割线性定价法之股票买卖时点计量 21
4 上证指数（深证成指）与股票相关性分析 31
结 论 33
课题展望及不足之处 34
——本课题的展望 34
——本文的不足之处 34
致 谢 35
参 考 文 献 36
19000多字
摘要 通过构建金融学中未定权益空间与线性空间间的对应关系，利用线性空间的性质特征等研究满足一价定律的金融市场等价于线性定价法则之事实，研究有价证券（债券、股票等）的无套利资产定价问题。
考虑到现有的线性定价法则大都较为抽象，难以为初学者理解和应用，正是基于这一问题的考量，本文拟透过探究有限维向量空间上线性定价函数的基本特征，提出并研究了基于黄金分割法下的线性定价函数，同时给出了其相应的应用研究。
首先，由金融学中的线性定价法则及数学中的黄金分割率给出了黄金分割线性定价法的定义；其次，简单介绍其一些性质；最后，给出了基于黄金分割法的国债及股票的实证分析。
实证结果表明：本文给出的黄金分割线性定价法对于债券、股票等有价证券买卖时点选择的研究结论是有效、合理的，具有一定的理论和实际意义。
关键词: 未定权益空间 线性定价函数 黄金分割线性定价法
Characteristics and application of linear pricing functions in finite dimensional vector space
Abstract By building in finance contingent claim corresponding relationship between space and linear space, by using the properties of linear space characteristics research meet the law of one price the fact of the financial markets is equivalent to the linear pricing law, the securities (bonds, stocks, etc.) no arbitrage asset pricing problem.
Considering the existing linear pricing rules are rather abstract, difficult to understand for beginners and applications, it is based on the consideration of the problem, this paper intends to explore the finite dimensional vector space through on the basic characteristics of the linear pricing function, put forward and studied based on the linear pricing function under the golden section method, and presents the corresponding application research.
First of all, by the finance of the golden ratio in linear pricing principle and mathematical definition of golden mean linear pricing is presented; Secondly, the simple introduction to some of its properties; Finally, based on the golden section method is given and the empirical analysis of the stock of public debt.
The empirical results show that: in this paper the golden linear pricing for bonds, stocks and other securities trading point selected research conclusion is reasonable and effective, has a certain theoretical and practical significance.
Keywords Contingent claims space The linear pricing function The golden section linear pricing
目 次
1 引言 1
1.1 选题的背景 1
1.2 研究现状 1
1.3 本文的创新点 2
2 金融学中的基本数学知识 4
2.1 有限维线性空间 4
2.2 有限维未定权益空间的完全市场和不完全市场 6
2.3 有限维未定权益空间上的线性定价法 9
2.4 线性定价函数的特征 15
3 有限维向量空间上黄金分割线性定价函数及其应用 17
3.1 定价之黄金分割法 17
3.2 黄金分割线性定价法则应用 18
3.2.1 黄金分割线性定价之国债买卖选择时点计量 18
3.2.2 黄金分割线性定价法之股票买卖时点计量 21
4 上证指数（深证成指）与股票相关性分析 31
结 论 33
课题展望及不足之处 34
——本课题的展望 34
——本文的不足之处 34
致 谢 35
参 考 文 献 36
