Kybernetika 48 no. 1, 130-143, 2012

Bounds of general Fréchet classes

Jaroslav Skřivánek

Abstract:

This paper deals with conditions of compatibility of a system of copulas and with bounds of general Fr\'{e}chet classes. Algebraic search for the bounds is interpreted as a solution to a linear system of Diophantine equations. Classical analytical specification of the bounds is described.

Keywords:

copula, Fréchet class, Diophantine equation

Classification:

60E05, 62H20, 11D45

paper.pdf

References:

  1. F. Durante, E. P. Klement and J. J. Quesada-Molina: Bounds for trivariate copulas with given bivariate marginals. J. Inequal. Appl. ID 161537 (2008).   CrossRef
  2. P. Embrechts, F. Lindskog and A. McNeil: Modelling dependence with copulas and applications to risk management. In: Handbook of Heavy Tailed Distributions in Finance (S. T. Rachev, ed.), Elsevier/North-Holland 2003.   CrossRef
  3. P. Embrechts: Copulas: A personal view. J. Risk Insurance 76 (2009), 3, 639-650.   CrossRef
  4. H. Joe: Multivariate models and Dependence Concepts. Chapman\&Hall, London 1997.   CrossRef
  5. R. B. Nelsen: Introduction to Copulas. Springer-Verlag, New York 2006.   CrossRef
  6. C. Genest and J. Nešlehová: A primer on copulas for count data. Astin Bull. 37 (2007), 2, 475-515.   CrossRef
  7. A. P. Tomás and M. Filgueiras: An algorithm for solving systems of linear Diophantine equations in naturals. In: Progress in Artificial Intelligence - EPIA'97, Lecture Notes in Artificial Intelligence 1323 (E. Costa and A. Cardoso, eds.), Springer-Verlag 1997, pp. 73-84.   CrossRef