曼德尔布罗特分形市模型分析
发布时间：2022-08-23 17:33
这篇论文是关于一个股票时间序列新模型的研究。一九九七年,曼德尔布罗特（BenoitMandelbrot）提出了这个新股票模型。Mandelbrot主要用分形理论模仿真正的股票时间序列。我的论文研究的一个目的就是说明为什么分形理论在金融市场（股票,国际兑换率和商品指数等）方面是有效的。这个新股票模型引入了新的分析工具。其中,赫斯特（Hurst）指数和R/S分析就是Mandelbrot模型的重要工具。这篇论文的另一个目的就是研究清楚这两个工具。最后,我将在论文用中国股票时间序列,国际兑换率和商品指数三项金融市场指数来验证这个新模型的有效性。 这篇论文主要分为4个部分。第一个部分是关于经典和新股票时间序列的模型的,主要是介绍这些模型创造的理由和新旧两个模型的比较。第二部分是对曼德尔布罗特引入的两个重要工具的研究:赫斯特指数和R/S分析。这个部分主要说明它们的特点和有效性。第三个部分是关于Mandelbrot的新股票模型的研究。这个部分说明怎么样利用这个新的模型真正创造一个时像真实的股票时间序列。最后一个部分包括所有数据试验的结果（模型比较,Hurst指数的计算和说明,Hurst指数的...
【文章页数】：51 页
【学位级别】：硕士
【文章目录】：
Abstract
详细摘要
1 Models of market
1.1 Market Theories
1.2 Classic model of stock time series
1.2.1 Random Walk
1.2.2 Brownian Motion
1.2.3 Arbitrage Theorem
1.2.4 Black-Scholes Formula
1.3 Limits of classic model
1.4 Fractals in Markets
1.4.1 Non independence
1.4.2 Turbulence
2 Hurst Coefficient,R/S Analysis
2.1 History and Main Idea
2.2 Hurst Exponent and Fractal Dimension
2.2.1 Self-similar Processes
2.2.2 Fractional Brownian Motion
2.2.3 Correlation function properties
2.2.4 Long-range dependence
2.3 R/S Analysis
2.3.1 Independent Processes
2.3.2 R/S Analysis
2.3.3 Hurst Exponent
2.3.4 Efficiency
3 Building Mandelbrot's Model
3.1 Ideas
3.2 Generator
3.2.1 Unit Generators
3.2.2 Turbulence
3.2.3 Hurst parameter
3.3 Multifractality
3.3.1 Relation between generators
3.3.2 Mathematical terms
4 Experiments on Data
4.1 Difference between models and reality
4.1.1 Independence/dependence
4.1.2 Normality
4.1.3 Correlation
4.2 Real Stock Hurst coefficient
4.2.1 Hurst computed
4.2.2 Findings
4.2.3 Explanation
4.3 Predictability
4.3.1 Goals and ideas
4.3.2 Results
4.4 Close looks on the RS Analysis
4.5 Conclusion
Appendix A Thanks and Statement
Appendix B References
B.1 Books and papers
B.2 Web resources
Appendix C Matlab
C.1 RS Analysis
C.2 Recherche Possible Evolutions
C.3 Other codes
本文编号：3678192
【文章页数】：51 页
【学位级别】：硕士
【文章目录】：
Abstract
详细摘要
1 Models of market
1.1 Market Theories
1.2 Classic model of stock time series
1.2.1 Random Walk
1.2.2 Brownian Motion
1.2.3 Arbitrage Theorem
1.2.4 Black-Scholes Formula
1.3 Limits of classic model
1.4 Fractals in Markets
1.4.1 Non independence
1.4.2 Turbulence
2 Hurst Coefficient,R/S Analysis
2.1 History and Main Idea
2.2 Hurst Exponent and Fractal Dimension
2.2.1 Self-similar Processes
2.2.2 Fractional Brownian Motion
2.2.3 Correlation function properties
2.2.4 Long-range dependence
2.3 R/S Analysis
2.3.1 Independent Processes
2.3.2 R/S Analysis
2.3.3 Hurst Exponent
2.3.4 Efficiency
3 Building Mandelbrot's Model
3.1 Ideas
3.2 Generator
3.2.1 Unit Generators
3.2.2 Turbulence
3.2.3 Hurst parameter
3.3 Multifractality
3.3.1 Relation between generators
3.3.2 Mathematical terms
4 Experiments on Data
4.1 Difference between models and reality
4.1.1 Independence/dependence
4.1.2 Normality
4.1.3 Correlation
4.2 Real Stock Hurst coefficient
4.2.1 Hurst computed
4.2.2 Findings
4.2.3 Explanation
4.3 Predictability
4.3.1 Goals and ideas
4.3.2 Results
4.4 Close looks on the RS Analysis
4.5 Conclusion
Appendix A Thanks and Statement
Appendix B References
B.1 Books and papers
B.2 Web resources
Appendix C Matlab
C.1 RS Analysis
C.2 Recherche Possible Evolutions
C.3 Other codes
本文编号：3678192
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