Multivariate Tail Risk Measures For Elliptical Distribution And Skew Normal Distribution

With the continuous development of China's insurance industry and the growing com-plexity of the financial environment,how to optimize risk management of investment port-folio is a problem that all kinds of financial institutions have to face.As an important part of risk management,risk measurement was mainly to study the mean-variance of assets to measure the risks faced by assets and their corresponding expected returns.The traditional mean-variance model can only describe the frequency and dispersion of risks.In recent years,more and more scholars have paid attention to the asymmetry and thick-tail phenomenon of financial asset fluctuations.They have begun to analyze the risk premia problem of assets of skewness and kurtosis to analyze the shape of a real data,that improves the accuracy of risk prediction for the future.In addition,it is necessary to construct a flexible multivariate distribution to analyze the impact of the correlation of loss rate among risks.In this thesis,starting from the basic theory of risk measurement,we summarize the previous research results of multivariate tail conditional expectation and multivariate-tail condition variance,further study the multivariate tail conditional of high-order moment risk measurement for elliptical distribution and skew-normal distribution,and give multivariate risk measurement expressions of two types of commonly elliptic distribution and skew-normal distribution.First,we introduce the definitions and properties of multivariate elliptical dis-tribution family and skew-normal distribution.The reason why we choose to use elliptical distribution model are that most elliptical distribution has obvious heavy tail characteristics,and the probability curve conforms to the general law of risk or return.In reality,affected by many factors,the real data of loss of risk is asymmetrical prominently.Fitting loss data with skew-normal distribution can get more closely approximates the shape of the real data,and retain more complete data information.Then,taking multivariate normal distribution and multivariate Pearson type VII distribution for instance,we give the concrete expres-sions of multivariate risk measure for the elliptical distribution family,and get numerical simulation by using Monte Carlo method to generate random number.Finally,we give the tail-conditional risk measurement expressions for skew-normal distributions in the univariate and multivariate cases.