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Characterization of dependence of multidimensional Lévy processes using Lévy copulas

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  • Kallsen, Jan
  • Tankov, Peter

Abstract

This paper suggests Lévy copulas in order to characterize the dependence among components of multidimensional Lévy processes. This concept parallels the notion of a copula on the level of Lévy measures. As for random vectors, a version of Sklar's theorem states that the law of a general multivariate Lévy process is obtained by combining arbitrary univariate Lévy processes with an arbitrary Lévy copula. We construct parametric families of Lévy copulas and prove a limit theorem, which indicates how to obtain the Lévy copula of a multivariate Lévy process X from the ordinary copula of the random vector Xt for small t.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 97 (2006)
Issue (Month): 7 (August)
Pages: 1551-1572

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Handle: RePEc:eee:jmvana:v:97:y:2006:i:7:p:1551-1572

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Related research

Keywords: Lévy process Copula Limit theorems;

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Cited by:
  1. Rosario Romera & Elisa M. Molanes, 2008. "Copulas in finance and insurance," Statistics and Econometrics Working Papers, Universidad Carlos III, Departamento de Estadística y Econometría ws086321, Universidad Carlos III, Departamento de Estadística y Econometría.
  2. Leisen, Fabrizio & Lijoi, Antonio, 2011. "Vectors of two-parameter Poisson-Dirichlet processes," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 102(3), pages 482-495, March.
  3. Fabrizio Leisen & Antonio Lijoi, 2010. "Vectors of two-parameter Poisson-Dirichlet processes," Quaderni di Dipartimento, University of Pavia, Department of Economics and Quantitative Methods 119, University of Pavia, Department of Economics and Quantitative Methods.
  4. Grothe, Oliver & Nicklas, Stephan, 2013. "Vine constructions of Lévy copulas," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 119(C), pages 1-15.
  5. Naoufel El-Bachir, 2008. "Dependent jump processes with coupled Lévy measures," ICMA Centre Discussion Papers in Finance, Henley Business School, Reading University icma-dp2008-03, Henley Business School, Reading University.
  6. N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 471-500, September.
  7. Nicole Bäuerle & Anja Blatter & Alfred Müller, 2008. "Dependence properties and comparison results for Lévy processes," Computational Statistics, Springer, Springer, vol. 67(1), pages 161-186, February.
  8. W. Zhu & Frabrizio Leisen, 2013. "A multivariate extension of a vector of Poisson- Dirichlet processes," Statistics and Econometrics Working Papers, Universidad Carlos III, Departamento de Estadística y Econometría ws132220, Universidad Carlos III, Departamento de Estadística y Econometría.
  9. Antonis Papapantoleon, 2011. "Computation of copulas by Fourier methods," Papers 1108.1216, arXiv.org, revised Jun 2014.
  10. N. Reich & C. Schwab & C. Winter, 2010. "On Kolmogorov equations for anisotropic multivariate Lévy processes," Finance and Stochastics, Springer, vol. 14(4), pages 527-567, December.
  11. Oliver Grothe & Stephan Nicklas, 2012. "Vine Constructions of Levy Copulas," Papers 1207.4309, arXiv.org, revised Sep 2012.
  12. Bäuerle, Nicole & Blatter, Anja, 2011. "Optimal control and dependence modeling of insurance portfolios with Lévy dynamics," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 398-405, May.
  13. Ilenia Epifani & Antonio Lijoi, 2009. "Nonparametric Priors for Vectors of Survival Functions," Quaderni di Dipartimento, University of Pavia, Department of Economics and Quantitative Methods 098, University of Pavia, Department of Economics and Quantitative Methods.

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