扩展熵优化理论及其在投资组合中的应用

发布时间：2018-01-19 01:35

本文关键词： 反熵广义熵风险厌恶程度证券投资组合　出处：《辽宁科技大学》2012年硕士论文　论文类型：学位论文

【摘要】：针对日益复杂的国际及国内政治经济形势，金融市场面临着巨大机遇与挑战。证券投资者如何在此环境背景下，将所受风险降到最低，从而获取预期收益，已经成为投资者亟需解决的问题之一，理智投资者通常选择组合方式进行投资，通过分散化选取股票以达到降低风险的目的，因此对于证券投资组合中风险的研究已逐渐成为学术界所面临的重大课题之一。传统证券投资组合理论以美国经济学家Harry Markowitz为依据，通过不断对其补充、完善使该模型更加符合投资者的决策需求。围绕着投资风险的度量问题，，熵优化理论已经并逐步被学者关注，该理论能够较好地度量投资风险，从而弥补传统投资组合模型的不足，本文正是在现有熵优化理论基础上，通过对反熵优化问题及广义熵优化问题进行探讨，首先将熵优化理论进行扩展，并依此构建了证券投资组合中的反熵优化模型及广义熵优化模型，同时将投资者对风险的厌恶程度定量化，使得熵优化理论更贴近投资者的投资偏好，更加满足投资者的投资意愿。全文共分六章节进行阐述，具体安排如下：第一章首先介绍了本文的选题背景与选题意义，然后将证券投资组合的理论沿革与该领域较为认可的模型一一列举，最后阐述了本文的创新点；第二章主要对熵优化理论进行较为全面地分析，首先谈及熵优化理论及演变过程，然后论及到几种较重要的熵定律，最后指出熵优化理论在证券投组合领域应用的适用性及可行性；第三章从物理学及数学中的反问题入手，定义了熵优化理论中的反熵问题，通过反熵模型的构建，指出反熵优化模型可以有序化度量风险，并且可以为投资者提供必要的证券行业选择需求；第四章在第三章选取行业的前提下，通过对Csisizer定向散度地分析，提出了考虑投资者风险厌恶程度的广义熵优化模型，并且通过实证分析，对投资者的个股投资提供了更有效地选择依据；第五章对反熵优化模型及广义熵优化模型进行对比分析，通过对二者适用范围的不同解释，为投资者进行下一步投资提供客观参考；第六章对全文进行总结，通过对本文所构建模型中出现的不足提出下一步研究工作的展望，从而完成本篇硕士论文的写作。
[Abstract]:In view of the increasingly complex international and domestic political and economic situation, the financial market is facing great opportunities and challenges. In this background how environmental securities investors, the risk to a minimum, in order to obtain the expected return, investors have become one of the urgent problems, rational investors usually choose combination investment, through decentralization of shares to select to reduce the risk, so the risk of the portfolio investment has gradually become one of the major issues faced by the academic circles.
The traditional portfolio theory by American economist Harry Markowitz as the basis, through continuous complement, perfect the model more in line with the decisions of investors demand. Measure around the investment risk, entropy optimization theory has been gradually concerned by academics, this theory to measure the investment risk effectively, so as to compensate for the lack of traditional portfolio the model, this paper is based on the theory of entropy in the existing optimization, through the anti entropy optimization problem and generalized entropy optimization problems are discussed, the entropy optimization theory is extended, and then constructs the investment portfolio in the anti entropy optimization model and generalized entropy optimization model, the quantitative risk aversion of investors the entropy, closer to the investors' preference optimization theory, and more to meet investors' willingness to invest. The thesis is divided into six chapters, the specific. Row as follows:
The first chapter introduces the background and significance of the topic, then lists the theoretical evolution of the portfolio and the more recognized models in the field, and finally expounds the innovation of this paper.
The second chapter mainly analyzes the theory of entropy optimization. First, we talk about entropy optimization theory and evolution process. Then we discuss several important entropy laws. Finally, we point out the applicability and feasibility of entropy optimization theory in the field of portfolio selection.
The third chapter starts from the inverse problems in physics and mathematics, defines the inverse entropy problem in entropy optimization theory, and points out that the counter entropy optimization model can ordinal risk measurement and provide necessary investors' choice for securities industry through the construction of anti entropy model.
In the fourth chapter, in the third chapter, based on the premise of choosing the industry, by analyzing the directional dispersion of Csisizer, we propose a generalized entropy optimization model considering the degree of risk aversion of investors, and provide a more effective basis for investors' individual stock investment through empirical analysis.
The fifth chapter analyzes the anti entropy optimization model and the generalized entropy optimization model, and provides an objective reference for investors to further invest by explaining the scope of application of the two.
The sixth chapter summarizes the full text, and puts forward the prospect of next research work through the shortcomings of the model built in this paper, so as to finish writing this master's thesis.

【学位授予单位】：辽宁科技大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F830.59;F224

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