The Theory Of Statistics Of Extremes And Its Applications In Risk Management

In the technic time, people benefit from the information society. On theother hand, they have to take on various risks induced by extreme events.These extreme events are not completely dependent, but in a way, almost allextreme events have some dependence. This paper mainly talks about thetheory of Statistics of Extremes and its applications in risk management.Measure of concordance is an ideal index that describes the dependencebetween two variables. For continuous random variable, measure of concor-dance is only related to Copula, while it is independent of marginal distri-butions; for discrete random variable, however, this conclusion is not valid.This paper induces the general formula which computes concordance measurebetween any two discrete random variables, it also talks about the way to com-pute the concordance measure between minimal and maximal order statistics.In addition, it analysis reasons why concordance measure between discreterandom variables is related to marginal distributions.During the analysis of finance risk, people usually come up against thecase that loss and income are asymmetric. Therefore, they should pay atten-tion to measurement of asymmetry. This paper puts forward a method whichmeasures radially asymmetry, provides the concept of maximal radially asym-metric Copula. Through constructing four singular Copulas, it also classifiesmaximal radially asymmetrical Copula to four sorts among which each classcrosses two given points. In addition, this paper explores the properties ofmaximal radially asymmetric Copula.Bases on the further study of univariate Extreme and Copula theory,this paper founds the threshold model of stationary sequence,multiplemeta-t distribution and multiple threshold model, studies their applicationsin network ?ow control,deciding insurance reserve and analyzing the risk ofexchange rate yield, respectively. First of all, it establishes the distribution of network ?ow according to threshold model. Subsequently, situation of network?ow can be researched, inspected and controlled real time, further to avoidnetwork blowing up. This model provides credible evidences for assigningbandwidth of network ?ow. Then, it uses combination of Pareto distributionand Log-normal distribution as marginal distribution, uses t-Copula asthe dependent structure among insurance operations, constructs the jointdistribution among insurance operations. According to this distribution,reserve of insurance formula can be computed. Compared with traditionalmethod, this method can reduce at least ten percents of reserve for insurancecompany and attains the purposes that avoids risk and saves fund. Lastly,through combining univariate excess threshold distribution and nonsymmetriclogistic Copula, this paper constructs multiple threshold model. Under thecase of excess threshold, this paper gains the joint distribution of yields oftwo exchange rates. According to this, the trend of two exchange rates canbe analyzed and predicted.