Advanced Search
MyIDEAS: Login

Distortions of multivariate risk measures: a level-sets based approach

Contents:

Author Info

  • Elena Di Bernardino

    ()
    (CEDRIC - Centre d'Etude et De Recherche en Informatique du Cnam - Conservatoire National des Arts et Métiers (CNAM))

  • Didier Rullière

    ()
    (SAF - Laboratoire de Sciences Actuarielle et Financière - Université Claude Bernard - Lyon I : EA2429)

Abstract

In this paper, we propose a parametric model for multivariate distributions. The model is based on distortion functions, i.e. some transformations of a multivariate distribution which permit to generate new families of multivariate distribution functions. We derive some properties of considered distortions. A suitable proximity indicator between level curves is introduced in order to evaluate the quality of candidate distortion parameters. Using this proximity indicator and properties of distorted level curves, we give a specific estimation procedure. The estimation algorithm is mainly relying on straightforward univariate optimizations, and we finally get parametric representations of both multivariate distribution functions and associated level curves. Our results are motivated by applications in multivariate risk theory. The methodology is illustrated on real examples.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://hal.archives-ouvertes.fr/docs/00/75/63/87/PDF/DiBernardino_Rulliere_2012.pdf
Download Restriction: no

Bibliographic Info

Paper provided by HAL in its series Working Papers with number hal-00756387.

as in new window
Length:
Date of creation: 12 Nov 2012
Date of revision:
Handle: RePEc:hal:wpaper:hal-00756387

Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00756387
Contact details of provider:
Web page: http://hal.archives-ouvertes.fr/

Related research

Keywords: Multivariate probability distortions; Level sets estimation ; Iterated compositions; Hyperbolic conversion functions ; Multivariate risk measures.;

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Biernacki, Christophe & Celeux, Gilles & Govaert, Gerard, 2003. "Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 561-575, January.
  2. Chacón, José E. & Rodríguez-Casal, Alberto, 2010. "A note on the universal consistency of the kernel distribution function estimator," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1414-1419, September.
  3. Alexis Bienven�e & Didier Rulli�re, 2012. "Iterative Adjustment of Survival Functions by Composed Probability Distortions," The Geneva Risk and Insurance Review, Palgrave Macmillan, vol. 37(2), pages 156-179, September.
  4. Belzunce, F. & Castano, A. & Olvera-Cervantes, A. & Suarez-Llorens, A., 2007. "Quantile curves and dependence structure for bivariate distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 5112-5129, June.
  5. Dehaan, L. & Huang, X., 1995. "Large Quantile Estimation in a Multivariate Setting," Journal of Multivariate Analysis, Elsevier, vol. 53(2), pages 247-263, May.
  6. Embrechts, Paul & Puccetti, Giovanni, 2006. "Bounds for functions of multivariate risks," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 526-547, February.
  7. Valdez, Emiliano A., 2009. "On the Distortion of a Copula and its Margins," MPRA Paper 20524, University Library of Munich, Germany.
  8. Areski Cousin & Elena Di Bernadino, 2013. "On Multivariate Extensions of Value-at-Risk," Working Papers hal-00638382, HAL.
  9. Obereder, Andreas & Scherzer, Otmar & Kovac, Arne, 2007. "Bivariate density estimation using BV regularisation," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5622-5634, August.
  10. Areski Cousin & Elena Di Bernadino, 2011. "On Multivariate Extensions of Value-at-Risk," Papers 1111.1349, arXiv.org, revised Apr 2013.
Full references (including those not matched with items on IDEAS)

Citations

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:hal-00756387. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.