一类多元copula和拟copula的构造
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摘要
【目的】研究了具有共同对角面函数的一类多元copula和拟copula的构造。【方法】将已有文献中对角面的概念加以推广,然后定义了一种""运算,基于这种运算建立了构造多元copula和拟copula的方法。【结果】给出了一类具有共同对角面函数的多元copula和拟copula,以及这些copula的性质。【结论】为相关统计建模和金融分析提供了描述某种相依结构的框架。
[Purposes]In this paper,The construction of a class of multivariate copulas and quasi-copulas is investigated with the common diagonal section function.[Methods]The notion of diagonal section on the former literature is generalized,and an operation is put forward which is denoted by "".Then based on this operation,a method of the construction of multivariate copulas and quasi-copulas is studied.[Findings]A class of multivariate copulas and quasi-copulas with the common diagonal section function is given,and its properties is discussed.[Conclusions]These provide some dependence frame for statistical modeling and financial analysis.
[Purposes]In this paper,The construction of a class of multivariate copulas and quasi-copulas is investigated with the common diagonal section function.[Methods]The notion of diagonal section on the former literature is generalized,and an operation is put forward which is denoted by "".Then based on this operation,a method of the construction of multivariate copulas and quasi-copulas is studied.[Findings]A class of multivariate copulas and quasi-copulas with the common diagonal section function is given,and its properties is discussed.[Conclusions]These provide some dependence frame for statistical modeling and financial analysis.
引文
[1]NELSEN R.An Introduction to copulas[M].2nd ed.NewYork:Springer,2006.
[2]JOE H.Multivariate models and dependenceconcepts[M].London:Chapman&Hall,1997.
[3]JOE H.Dependence modeling with copula[M].NewYork:CRC Press,2014.
[4]DENUIT M,DHAENE J,GOOVAERTS M,et al.Actuarial theory for dependence risk:measures orders and models[M].Hoboken:JohnWiley&Sons,2005.
[5]ANE T,KHAROUBI C.Depedence structure and risk measure[J].Journal of Business,2003,76(3):411-438.
[6]MALEVERGNE Y,SORNETTE D.Extreme financial risk:from dependence to risk management[M].Berlin:Springer-Verlag,2006.
[7]CHAN Y,LI H.Tail dependence for multivariate t-copulas and its monotonicity[J].Insurance:Mathematics and Economics,2008,42(2):763-770.
[8]ALSINA C,NELSEN R B.On the characterization of a class of binary operations on distribution functions[J].Statistics&Probability Letters,1993,17(2):85-89.
[9]FURMAN E,KUZNETSOV A,SU J,et al.Tail dependence of the Gaussian copula revisited[J].Insurance:Mathematics and Economics,2016,69:97-103.
[10]FERNANDEZ-SANCHEZ J,NELSEN R,QUESADAMOLINA,et al.Independence results for multivariate tail dependence coeffecients[J].Fuzzy Sets and Systems,2015,284:129-137.
[11]AMO E,MEYER H,CARRILLO M,et al.Characterization of copulas with given diagonal and opposite diagonal sections[J].Fuzzy Sets and Systems,2014,284:63-77.
[12]BERNARDINO E,RULLIRE D.On tail dependence coeffecients of transformed multivariate Archimedean copulas[J].Fuzzy Sets and Systems,2016,284:89-112.
[13]GENEST C,MOLINA J,SEMPI C.A characerization of quasi-copulas[J].Journal of Multivariate Analysis,1999,69(2):193-205.
[14]CUCULESCU I,THEODORESCU R.Copulas:diagonals and tracks[J].Rev Roumaine Math Pures Appl,2001,46:731-742.
[15]NELSEN R,MOLINA J,LALLENA J,et al.Best-possible bounds on sets of bivariate distribution functions[J].Journal of Multivariate Analysis,2004,90(2):348-358.
[16]曾霞,何平.基于g函数的多元copula的构造[J].数理统计与管理,2008,27(5):843-849.ZENG X,HE P.Construction of n-copula dependence on gfunction[J].Appliction of Statistics and Management,2008,27(5):843-849.
[2]JOE H.Multivariate models and dependenceconcepts[M].London:Chapman&Hall,1997.
[3]JOE H.Dependence modeling with copula[M].NewYork:CRC Press,2014.
[4]DENUIT M,DHAENE J,GOOVAERTS M,et al.Actuarial theory for dependence risk:measures orders and models[M].Hoboken:JohnWiley&Sons,2005.
[5]ANE T,KHAROUBI C.Depedence structure and risk measure[J].Journal of Business,2003,76(3):411-438.
[6]MALEVERGNE Y,SORNETTE D.Extreme financial risk:from dependence to risk management[M].Berlin:Springer-Verlag,2006.
[7]CHAN Y,LI H.Tail dependence for multivariate t-copulas and its monotonicity[J].Insurance:Mathematics and Economics,2008,42(2):763-770.
[8]ALSINA C,NELSEN R B.On the characterization of a class of binary operations on distribution functions[J].Statistics&Probability Letters,1993,17(2):85-89.
[9]FURMAN E,KUZNETSOV A,SU J,et al.Tail dependence of the Gaussian copula revisited[J].Insurance:Mathematics and Economics,2016,69:97-103.
[10]FERNANDEZ-SANCHEZ J,NELSEN R,QUESADAMOLINA,et al.Independence results for multivariate tail dependence coeffecients[J].Fuzzy Sets and Systems,2015,284:129-137.
[11]AMO E,MEYER H,CARRILLO M,et al.Characterization of copulas with given diagonal and opposite diagonal sections[J].Fuzzy Sets and Systems,2014,284:63-77.
[12]BERNARDINO E,RULLIRE D.On tail dependence coeffecients of transformed multivariate Archimedean copulas[J].Fuzzy Sets and Systems,2016,284:89-112.
[13]GENEST C,MOLINA J,SEMPI C.A characerization of quasi-copulas[J].Journal of Multivariate Analysis,1999,69(2):193-205.
[14]CUCULESCU I,THEODORESCU R.Copulas:diagonals and tracks[J].Rev Roumaine Math Pures Appl,2001,46:731-742.
[15]NELSEN R,MOLINA J,LALLENA J,et al.Best-possible bounds on sets of bivariate distribution functions[J].Journal of Multivariate Analysis,2004,90(2):348-358.
[16]曾霞,何平.基于g函数的多元copula的构造[J].数理统计与管理,2008,27(5):843-849.ZENG X,HE P.Construction of n-copula dependence on gfunction[J].Appliction of Statistics and Management,2008,27(5):843-849.