On the distortion of a copula and its margins

References

• Bäuerle , N. 1997 . Inequalities for stochastic models via supermodular orderings . Stochastic Models , 13 : 181 – 201 .
   Google Scholar
• Blum , P. , Dias , A. and Embrechts , P. 2002 . “ The ART of dependence modelling: the latest advances in correlation analysis ” . In Alternative risk strategies , Edited by: Lane , M. 339 – 356 . London : Risk Books .
   Google Scholar
• Cherubini , U. , Luciano , E. and Vecchiato , W. 2004 . Copula methods in finance , West Sussex , , UK : John Wiley .
   Google Scholar
• Crane , G. and van der Hoek , J. 2008 . Using distortion of copulas to price synthetic CDOs . Insurance: Mathematics and Economics , 42 : 903 – 908 .
   Web of Science ®Google Scholar
• Denuit , M. , Dhaene , J. , Goovaerts , M. and Kaas , R. 2005 . Actuarial theory of dependent risks , West Sussex , , UK : John Wiley .
   Google Scholar
• Feller , W. 1971 . An introduction to probability theory and its applications , Vol. 2 , New York : John Wiley .
   Google Scholar
• Frees , E. W. and Valdez , E. A. 1998 . Understanding relationships using copulas . North American Actuarial Journal , 2 : 1 – 25 .
   Google Scholar
• Genest , C. and Rivest , L.-P. 2001 . On the multivariate probability integral transformation . Statistics and Probability Letters , 53 : 391 – 399 .
   Web of Science ®Google Scholar
• Joe , H. 1997 . Multivariate models and dependence concepts , Boca Raton , FL : Chapman and Hall .
   Google Scholar
• Kijima , M. 2006 . A multivariate extension of equilibrium pricing transforms: the multivariate Esscher and Wang transforms for pricing financial and insurance risks . ASTIN Bulletin , 36 : 269 – 283 .
   Web of Science ®Google Scholar
• Klugman , S. A. and Parsa , R. 1999 . Fitting bivariate loss distributions with copulas . Insurance: Mathematics and Economics , 24 : 139 – 148 .
   Web of Science ®Google Scholar
• Landsman , Z. M. and Valdez , E. A. 2003 . Tail conditional expectations for elliptical distributions . North American Actuarial Journal , 7 : 55 – 71 .
   Google Scholar
• McNeil , A. J. , Frey , R. and Embrechts , P. 2005 . Quantitative risk management: concepts, techniques and tools , Princeton , NJ : Princeton University Press .
   Google Scholar
• Morillas , P. M. 2005 . A method to obtain new copulas from a given one . Metrika , 61 : 169 – 184 .
   Web of Science ®Google Scholar
• Müller , A. and Scarsini , M. 2000 . Some remarks on the supermodular order . Journal of Multivariate Analysis , 73 : 107 – 119 .
   Web of Science ®Google Scholar
• Nelsen , R. B. 2006 . An introduction to copulas , New York : Springer-Verlag .
   Google Scholar
• Roberts , A. W. and Varberg , D. E. 1973 . Convex functions , New York : Academic Press .
   Google Scholar
• Schmitz V. 2003 Copulas and stochastic processes Ph.D. Thesis, Institute of Statistics, Aachen University
   Google Scholar
• Sklar , A. 1959 . Fonctions de répartition à n dimensions et leurs marges . Publications de l'Institute de Statistique de L'Universite de Paris , 8 : 229 – 231 .
   Google Scholar
• Wang , S. S. 1996 . Premium calculation by transforming the layer premium density . ASTIN Bulletin , 21 : 71 – 92 .
   Google Scholar
• Wang , S. S. 2007 . Normalized exponential tilting: pricing and measuring multivariate risks . North American Actuarial Journal , 11 : 89 – 99 .
   Google Scholar
• Widder , D. V. 1946 . The laplace transform , Princeton , NJ : Princeton University Press .
   Google Scholar
• Yaari , M. E. 1987 . The dual theory of choice under risk . Econometrica , 55 : 95 – 115 .
   Web of Science ®Google Scholar