Gaussian approximation of conditional elliptical copulas

In this paper the limits of elliptical copulas under univariate conditioning are characterized, allowing for the conditioning random variable to have a rapidly varying tail. Further, we investigate the quality of approximation by imposing some weak asymptotic restrictions.

[1]  J. Hüsler,et al.  Asymptotics of a Boundary Crossing Probability of a Brownian Bridge with General Trend , 2003 .

[2]  N. Ng,et al.  Extreme values of ζ′(ρ) , 2007, 0706.1765.

[3]  Lei Si Ni Ke Resnick.S.I. Extreme values. regular variation. and point processes , 2011 .

[4]  Paul Embrechts,et al.  An EVT Primer for Credit Risk , 2011 .

[5]  S. Łojasiewicz,et al.  An introduction to the theory of real functions , 1988 .

[6]  H. Joe Multivariate models and dependence concepts , 1998 .

[7]  Wolfgang K. Härdle,et al.  De Copulis Non Est Disputandum - Copulae: An Overview , 2009 .

[8]  Threshold copulas and positive dependence , 2008 .

[9]  Gaussian Approximation of Conditional Elliptical Random Vectors , 2006 .

[10]  Wolfgang K. Härdle,et al.  De copulis non est disputandum , 2010 .

[11]  C. Sempi,et al.  Copula Theory: An Introduction , 2010 .

[12]  Paul Embrechts,et al.  The Devil is in the Tails: Actuarial Mathematics and the Subprime Mortgage Crisis , 2010, ASTIN Bulletin.

[13]  Mario V. Wüthrich,et al.  Tail Dependence from a Distributional Point of View , 2003 .

[14]  Andrew J. Patton Modelling Asymmetric Exchange Rate Dependence , 2006 .

[15]  Fabrizio Durante,et al.  Invariant dependence structure under univariate truncation , 2012 .

[16]  A. Juri,et al.  Limiting dependence structures for tail events, with applications to credit derivatives , 2006, Journal of Applied Probability.

[17]  A. Juri,et al.  Copula convergence theorems for tail events , 2002 .

[18]  S. Berman Sojourns and Extremes of Stochastic Processes , 1992 .

[19]  C. Klüppelberg,et al.  Modelling Extremal Events , 1997 .

[20]  E. Luciano,et al.  Copula methods in finance , 2004 .

[21]  G. Simons,et al.  On the theory of elliptically contoured distributions , 1981 .

[22]  R. Nelsen An Introduction to Copulas , 1998 .

[23]  Radko Mesiar,et al.  Univariate conditioning of copulas , 2008, Kybernetika.

[24]  Fabrizio Durante,et al.  Spatial contagion between financial markets: a copula-based approach , 2010 .

[25]  PAUL EMBRECHTS,et al.  Modelling of extremal events in insurance and finance , 1994, Math. Methods Oper. Res..

[26]  P. Jaworski Invariant dependence structure under univariate truncation: the high-dimensional case , 2013 .