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Copula Theory And Dependence Analysis

Posted on:2010-08-27Degree:DoctorType:Dissertation
Country:ChinaCandidate:J WuFull Text:PDF
GTID:1119360302971053Subject:Probability theory and mathematical statistics
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The present work concerns the study of the multivariable dependence using copula theory and its application.Copula is a kind of function that "connects" multivariate joint distribution and margins,and the major advantages are:first,it can characterize the multivariate dependent structure completely;Secondly,it can deal with the univariate margin and the dependent structure separately,and then integrate them,so that copula can generate a variety of flexible high-dimensional probability distribution.We analyze the characteristics of multivariate copula functions,and then discuss the dependence between variables based on copula theory.We also integrate the selection of multivariate copula parameter models,as well as getting some results about multivariate extreme value theory in terms of copula functions.Finally the applications of copula are considered in finance and insurance fields.The key points and main achievements of this thesis are listed as follows:1.The importance of copula theory on the multivariate dependence is given,and the advantages and characteristics are compared to the traditional methods.We discuss the different forms about Sklar theorem when the margins are continuous or not, and prove it easily by a new way.The relationship between Kendall'sτand Spearman'sρcoefficient is studied in terms of copula theory,and the inequalities about the changes of their ratioρ/τare verified.For a class of copulas with parameters,the limit of ratio is proved to be 3/2.2.How to select the appropriate copula to describe the multivariate dependent structure? It is a difficult problem in recent research.We select a special kind of copula which can only be decided by a unary function,so as to reduce the dimension. Giving the nature and graphics of such four copulas,goodness-of-fit tests are suggested within parameter is known or unknown.We make the empirical analysis of China's stock market.The results show that the Shanghai index and Shenzhen composite index share a strong positive dependence,and Gumbel copula is the most suitable in the dependent models.3.Multi-extreme theory is much complex,especially when variates are not independent. The extreme behavior of just one component of a random vector is unlikely to imply the extreme behavior of the whole vector.Therefore,the analysis about dependence plays an important role in the extreme value theory research and application areas such as finance and insurance in which tail dependence is particularly remarkable. For the financial data showing a leptokurtosis,thick tail and other characteristics, we get the tail dependence of multivariate maxima using a special kind of copula called extreme value copula,and the result is applied to the area relating to medical insurance large claims.We construct the model for calculating the cost of reinsurance. The results show that the plan for selecting the extreme value copula to calculate the costs is optimal in all programs.
Keywords/Search Tags:Copula, Dependence, Kendal'sτ, Spearman'sρ, Extreme Value Th-eory, Extreme Value Copula, Tail Dependence
PDF Full Text Request
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