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Strong Stability of Linear Forms of φ-Mixing Random Variables and Modify the Distribution Based on Distortion Function and the Estimation of VaR

Author: WangYue
Tutor: WanChengGao
School: Hubei University
Course: Probability Theory and Mathematical Statistics
Keywords: φ-mixing Strong stability linear form distortion function VaR parameter estimation non-parameter estimation
CLC: O212.1
Type: Master's thesis
Year: 2013
Downloads: 2
Quote: 0
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Abstract


In twentieth Century of thirty or forty time,the limit theory of independent random suquence has been perfectly developed, and gets a lot of achievements. Then,some scholars have been developed to extending these method to dependent case due to the widely existence of dependent random variables,and gets some re-sults, which arose lots of probability questions.The strong stability of linear forms is the promotion of classical strong law of large numbers,and had found many appli-cations in ecology,molecular biology,biochemistry etc.Therefore the research about the strong stability of linear forms is undoubtedly very important.In the paper,we investigate the strong stability of linear forms for φ mixing sequence. we first study the φ mixing sequence by using termination, then through Borel-Cantellilemma and properties of φ mixing sequence we taken the sufficient condition of the strong sta-bility of linear forms of φ mixing sequence in usual situation. Based on above result, we give results on the stability of other linear forms in φ mixing sequences.Influenced by the factor of financial innovation and market develops,huge changes are taking place in the financial market,and risks become more and more compli-cated.So the research and development of risk measurement models are our top priority.The emergence of Value at Risk enables us to quantify the maximum loss of financial portfolios in certain preiod.And it has become the fundation of finan-cial risk measurement system up to now. But it has a flaw:it doesn’t take all the information of the initial loss distribution into consideration,ignoring the risk of extreme events of the tail,high-risk events.In this paper,we study function risk measure,this type of risk measures in essence emphasizes the tail risk,which gives a greater weight to high-risk events through modifying the distribution.Since the distributions of financial data are heavy-tail generally,the distorted function was in-triduced to modify the normal distribution.The modified distribution could describe the fat tail distrbution better,so we could get more accurate estimator of VaR by this distorted distribution. we have put forward two methods to modify distortion distribution function:parameter and non-parameter estimation methods.Finally, we make a summary.

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CLC: > Mathematical sciences and chemical > Mathematics > Probability Theory and Mathematical Statistics > Mathematical Statistics > General mathematical statistics
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