Bounds of general Fréchet classes

Jaroslav Skřivánek

Kybernetika (2012)

  • Volume: 48, Issue: 1, page 130-143
  • ISSN: 0023-5954

Abstract

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This paper deals with conditions of compatibility of a system of copulas and with bounds of general Fréchet 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.

How to cite

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Skřivánek, Jaroslav. "Bounds of general Fréchet classes." Kybernetika 48.1 (2012): 130-143. <http://eudml.org/doc/246979>.

@article{Skřivánek2012,
abstract = {This paper deals with conditions of compatibility of a system of copulas and with bounds of general Fréchet 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.},
author = {Skřivánek, Jaroslav},
journal = {Kybernetika},
keywords = {copula; Fréchet class; Diophantine equation; copula; Fréchet bounds; Fréchet class; linear Diophantine equation},
language = {eng},
number = {1},
pages = {130-143},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Bounds of general Fréchet classes},
url = {http://eudml.org/doc/246979},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Skřivánek, Jaroslav
TI - Bounds of general Fréchet classes
JO - Kybernetika
PY - 2012
PB - Institute of Information Theory and Automation AS CR
VL - 48
IS - 1
SP - 130
EP - 143
AB - This paper deals with conditions of compatibility of a system of copulas and with bounds of general Fréchet 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.
LA - eng
KW - copula; Fréchet class; Diophantine equation; copula; Fréchet bounds; Fréchet class; linear Diophantine equation
UR - http://eudml.org/doc/246979
ER -

References

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  1. F. Durante, E. P. Klement, J. J. Quesada-Molina, Bounds for trivariate copulas with given bivariate marginals., J. Inequal. Appl. ID 161537 (2008). (2008) Zbl1162.62047MR2481572
  2. P. Embrechts, F. Lindskog, 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. (2003) 
  3. P. Embrechts, 10.1111/j.1539-6975.2009.01310.x, J. Risk Insurance 76 (2009), 3, 639-650. (2009) DOI10.1111/j.1539-6975.2009.01310.x
  4. H. Joe, Multivariate models and Dependence Concepts., Chapman&Hall, London 1997. (1997) Zbl0990.62517MR1462613
  5. R. B. Nelsen, Introduction to Copulas., Springer-Verlag, New York 2006. (2006) Zbl1152.62030MR2197664
  6. C. Genest, J. Nešlehová, 10.2143/AST.37.2.2024077, Astin Bull. 37 (2007), 2, 475-515. (2007) MR2422797DOI10.2143/AST.37.2.2024077
  7. A. P. Tomás, 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. (1323) MR1703009

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