×

zbMATH — the first resource for mathematics

Bounds of general Fréchet classes. (English) Zbl 1251.60015
The manuscript deals with multivariate copulas with given margins. First, a characterization is given for all copulas belonging to a Fréchet class in terms of the \(n\)-increasing property and some simple bounds. Then a method is presented for interpreting the search of the bounds of a general Fréchet class in terms of a solution of a linear system of Diophantine equations. As a byproduct, some analytic constructions of bounds are presented.

MSC:
60E05 Probability distributions: general theory
62H20 Measures of association (correlation, canonical correlation, etc.)
11D04 Linear Diophantine equations
PDF BibTeX XML Cite
Full Text: Link EuDML
References:
[1] F. Durante, E. P. Klement, J. J. Quesada-Molina: Bounds for trivariate copulas with given bivariate marginals. J. Inequal. Appl. ID 161537 (2008). · Zbl 1162.62047 · doi:10.1155/2008/161537 · eudml:129952 · arxiv:0711.2409
[2] P. Embrechts, F. Lindskog, A. McNeil: Modelling dependence with copulas and applications to risk management. Handbook of Heavy Tailed Distributions in Finance (S. T. Rachev, Elsevier/North-Holland 2003.
[3] P. Embrechts: Copulas: A personal view. J. Risk Insurance 76 (2009), 3, 639-650. · doi:10.1111/j.1539-6975.2009.01310.x
[4] H. Joe: Multivariate models and Dependence Concepts. Chapman&Hall, London 1997. · Zbl 0990.62517
[5] R. B. Nelsen: Introduction to Copulas. Springer-Verlag, New York 2006. · Zbl 1152.62030
[6] C. Genest, J. Nešlehová: A primer on copulas for count data. Astin Bull. 37 (2007), 2, 475-515. · Zbl 1274.62398 · doi:10.2143/AST.37.2.2024077
[7] A. P. Tomás, M. Filgueiras: An algorithm for solving systems of linear Diophantine equations in naturals. Progress in Artificial Intelligence - EPIA’97, Lecture Notes in Artificial Intelligence 1323 (E. Costa and A. Cardoso, Springer-Verlag 1997, pp. 73-84. · Zbl 0884.11020
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.