金融经济学中的组合数学问题

发布时间：2018-01-21 17:38

本文关键词： 组合分析理论市场问题组合投资问题单项基金分离现象　出处：《北京工业大学》2014年硕士论文　论文类型：学位论文

【摘要】：金融经济学中的问题由来已久，每个人、每个经济实体几乎每天都面临着一个组合决策问题。面对现实生活中大量的不确定性因素，特别是近年来重大金融突发事件的发生以及金融变革中的诸多问题，导致金融经济领域的研究环境越来越复杂，而组合数学的主要应用就是在各种复杂关系中找出最优的方案。在考虑现实生活中存在的各种金融组合问题，采用组合计数理论、组合最优化理论以及组合设计理论，分别研究市场中的组合问题，进而揭示其在现实应用中的意义。论文主要基于对组合与金融基础知识的研究，，进而探讨组合分析理论在市场中的应用。具体包括：分析普通商品市场问题，利用组合计数方法，简化市场问题求解过程中的证明；采用容斥原理，进一步证明了Beach,s原始问题。对金融市场组合投资中的基本知识进行研究，分析金融市场中组合投资优化问题，根据马科维茨均值方差模型，构造了在允许卖空的假设下股票的组合模型，并进行实例解析，帮助人们树立正确的投资理念；从资本资产定价模型出发，运用实例分析，探究组合证券券种选择的基本方法，帮助人们正确选择组合证券；分析套利定价模型的单因素模型，采用具体事例探究其在证券市场中的应用，帮助人们正确选择套利组合。详细推导并证明了单项基金分离现象成立的充分必要条件，然后进行实例分析，总结自己的结论。
[Abstract]:Long-standing problems in financial economics, each person, each economic entity almost every day facing a portfolio decision problem. To face the reality of life in a lot of uncertain factors, especially the problems in recent years, major financial events and financial reform, leading to financial and economic research in the field of environment more and more complex, the main application of combinatorial mathematics is to find the optimal solution in the complex relationship. In consideration of various combinations of financial problems exist in reality, using the combinatorial counting theory, optimization theory and design theory, study on combination of market respectively, and to explore its application in the real sense.
Study on the combination and the basic knowledge of financial papers is mainly based on the combination of theoretical analysis, and discusses the application in the market. Including: the analysis of the general commodity market, using a combination of counting method, a simplified proof of market in the process of solving problems; the principle of inclusion and exclusion, further proved that Beach, s of the basic knowledge of the original problem. The combination of financial market investment, analysis of investment combination optimization problem in the financial market, according to Markowitz mean variance model, constructed portfolio model under the assumption that the stock in short selling, and in the case analysis, to help people establish a correct concept of investment; starting from the capital asset pricing model, use case analysis, explore the basic method portfolio Quanzhong choice, help people choose the right portfolio; single factor analysis model, arbitrage pricing model, using specific examples. Its application in securities market helps people to choose Arbitrage Portfolios correctly. The necessary and sufficient conditions for the separation of single funds are derived and proved in detail. Then, an example is analyzed to summarize its conclusion.

【学位授予单位】：北京工业大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：O157;F830

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