Construction Of Extreme-value Copulas And Its Property

Extreme-value statistics has been the efective method to analyze extremeevents, and used widely in the realms of finance,insurance,hydrology, environmentand so on.Because of the complexity in the real world, extreme events tend to occursimultaneously and in succession, such as financial contagion, portfolio theoryand risk management,air pollution in diferent regions,more extreme weathers andso on. Therefore, multivariate extreme-value is becoming the theory front andresearch hotspot.In the theory of multivariate extreme-value, extreme-value copulas are indis-pensible analytical tool, which provides appropriate models for the dependencestructure between extreme events and indicate the multivariate extreme-valuedistribution cumulative function. One basic problem of the multivariate extreme-value statistics analysis is to construct the multivariate extreme-value distribu-tions, which is equivalent to constructing the extreme-value copulas. This papermainly uses products of copulas to generate extreme-value copulas. At first, themodel of construction is given. The model, which is consisted of some knowncopulas and a series of functions which is defined on the united interval, is limitedto the exponential function for its max-stable. Secondly, it discusses a propertyabout the bound of the new copulas and describes its model interpretation inthe special case.The result indicates that the standard convex combination of kcopulas is in the attraction domination which can be expressed by the weightedgeometric mean of their respective attraction dominations.The tail dependence measure is used to describe the co-movement of themultivariate random variables. This paper presents the upper-orthant tail de-pendence measure of the usual extreme-value copula. For the new extreme-valuecopulas, its explicit expressions are deprived, not only for the upper tail depen-dence coefcients of bivariate copulas, but also for the extensive version. Finally,taking Gumbel copula, maximum copula and independent copula as an example,two extreme-value copulas generating by the Gumbel copula and the two others, are analyzed. Their tail dependence and asymmetry of the dependence also areillustrated.