A Kind Of Ellipse Distribution And Its Application In Risk Management

On the one hand,since most of the theory and application of multivariate analysis are based on the multivariate normal distributions,researchers aim to develop the multivariate analysis based on the multivariate non-normal distributions.One of the methods is to find a family of multivariate distributions which possess similar properties with the multivariate normal distributions.Therefore,multivariate elliptically contoured distributions,overcoming the shortcomings of the normal distributions,are quite quality because of its convenient properties.On the other hand,risk measures,especially the multivariate risk measures,play an important role in risk management and actuarial applications.Nowadays,the properties of multivariate elliptically contoured distributions and its applications in risk measures become popular.However,most of the study focus on generalizing the properties of multivariate normal distributions in the multivariate elliptically contoured distributions and its applications in risk measures directly.Meanwhile,the multivariate elliptically contoured distributions with dimension incoherent,including the multivariate logistic distributions,the Kotz type distributions,and the multivariate exponential power distributions,are crucial in the risk management as well.But there are far less researches on this kind of distribution.There are lots of researches on the properties of multivariate elliptically contoured distributions and its applications in risk measures,in which many tractable properties are concluded.However,there are some inaccuracies as well.For example,in some researches,it believes that multivariate elliptically contoured distributions satisfy the dimension coherent.Therefore,the consistency properties are widely used in research on risk measures.However,elliptically contoured distributions such as logistic distributions and the Kotz type distributions are dimension inconsistency.The mistakenly use of dimension coherent in risk management may impact on insurance practice.Therefore,we study a new class of multivariate elliptically symmetric distributions with inconsistency properties including elliptically symmetric logistic distributions and Kotz type distributions which may develop the multivariate elliptically contoured distributions and risk measures system.The study on the properties of the new class of multivariate elliptically symmetric distributions is significative in theory and practice.We introduce a new class of multivariate elliptically symmetric distributions including elliptically symmetric logistic distributions and Kotz type distributions.We investigate the various probabilistic properties including density generators,marginal distributions,conditional distributions,moments,linear transformations,characteristic functions,characteristic generators and dependence measure in the perspective of the inconsistency property with the help of generalized Hurwitz-Lerch zeta function.We also study the multivariate tail risk measures of this new class of elliptically symmetric distributions and its applications in risk management.