非卖空投资组合选择问题的增广Lagrange函数方法

发布时间：2018-01-01 00:29

本文关键词：非卖空投资组合选择问题的增广Lagrange函数方法　出处：《大连理工大学》2013年硕士论文　论文类型：学位论文

【摘要】：投资组合的选择就是对金融资产进行量化分析,建立数学模型,在一定的分析框架下.制定出一定风险水平下的具有最高收益的投资策略.非卖空均值-方差投资组合选择问题是金融数学中的一个非常重要的研究课题,在市场非卖空的限制下：面对瞬息、万变的金融市场,投资者通过建立适当的数学模型,借助统计学的方法和计算机的数据处理能力,来制定最优的投资策略.非卖空的均值-方差投资组合模型是没有显示解的,很多优化算法可以用来求解这类问题,本文主要讨论的是增广Lagrange函数方法在求解一系列非卖空的均值-方差投资组合问题中的应用. 在本文的绪论部分,我们对投资组合选择的相关问题的研究背景和现状做了简单的阐述.第二章我们将结合具体例子讨论不同风险容忍度的投资者如何运用增广Lagrange函数方法.最大化投资组合收益.制定最优投资组合策略.随后我们对市场作了更细致的分析,第三章将在均值—方差分析的框架下,运用极大极小准则在最坏的情形下寻找最优投资策略,然后运用第二章中的增广Lagrange函数方法求得数值解并结合具体的例子加以说明.本文第四章将考虑市场的摩擦因素,在第三章模型假设的基础上,引入了税收和交易费等摩擦因素,然后结合例子讨论了在摩擦市场中的投资者是如何基于极大极小投资组合模型制定最优投资策略.
[Abstract]:Portfolio selection is to make quantitative analysis on financial assets, the establishment of mathematical model, the analysis framework of certain. Make certain risk level with the highest income investment strategy. The non short mean variance portfolio selection problem is a research topic is very important in mathematical finance, non short selling in the market the limit: the face of rapidly, the financial market, investors through the establishment of an appropriate mathematical model, data processing method and statistical ability with the aid of computer, to make the optimal investment strategy. No short sale mean variance portfolio model is no display solution, many optimization algorithms can be used to solve this problem, this paper the main discussion is the application of augmented Lagrange function method of investment in solving a series of non short mean variance portfolio problem.
In the introduction part, briefly introduces the research background and current situation of related problems of our choice of portfolio. In the second chapter, we will discuss the different risk tolerance of investors how to use the augmented Lagrange function method. The maximum portfolio income. Develop optimal portfolio strategies. Then we make on the market more detailed analysis, the third chapter in the mean variance analysis framework, using the minimax criterion to find the optimal investment strategy in the worst case, then using augmented Lagrange method in chapter second to obtain numerical solution and combined with specific examples. The fourth chapter will consider the friction factors of the market. In the third chapter based on the assumption of the model is introduced, such as tax and transaction costs of friction factors, and then combined with the examples discussed in the frictional market investors is how The optimal investment strategy is formulated based on the minimax investment portfolio model.

【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F830.59;F224

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