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Skewed bivariate models and nonparametric estimation for the CTE risk measure

  • Bolance, Catalina
  • Guillen, Montserrat
  • Pelican, Elena
  • Vernic, Raluca

In this paper, we illustrate the use of the Conditional Tail Expectation (CTE) risk measure on a set of bivariate real data consisting of two types of auto insurance claim costs. Several continuous bivariate distributions (normal, lognormal, skew-normal with the alternative log-skew-normal) are fitted to the data. Besides, a bivariate nonparametric transformed kernel estimation is presented. CTE formulas are given for all these, and numerical results on the real data are discussed and compared.

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Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

Volume (Year): 43 (2008)
Issue (Month): 3 (December)
Pages: 386-393

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Handle: RePEc:eee:insuma:v:43:y:2008:i:3:p:386-393
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505554

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  1. Vernic, Raluca, 2006. "Multivariate skew-normal distributions with applications in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 413-426, April.
  2. Adelchi Azzalini, 2005. "The Skew-normal Distribution and Related Multivariate Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 159-188.
  3. Barry Arnold & Robert Beaver & A. Azzalini & N. Balakrishnan & A. Bhaumik & D. Dey & C. Cuadras & J. Sarabia & Barry Arnold & Robert Beaver, 2002. "Skewed multivariate models related to hidden truncation and/or selective reporting," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 11(1), pages 7-54, June.
  4. Furman, Edward & Zitikis, Ricardas, 2008. "Weighted premium calculation principles," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 459-465, February.
  5. Gupta, Arjun K. & González-Farías, Graciela & Domínguez-Molina, J. Armando, 2004. "A multivariate skew normal distribution," Journal of Multivariate Analysis, Elsevier, vol. 89(1), pages 181-190, April.
  6. Bolance, Catalina & Guillen, Montserrat & Perch Nielsen, Jens, 2000. "Kernel Density Estimation of Actuarial Loss Functions," Finance Working Papers 00-4, University of Aarhus, Aarhus School of Business, Department of Business Studies.
  7. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  8. Furman, Edward & Landsman, Zinoviy, 2005. "Risk capital decomposition for a multivariate dependent gamma portfolio," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 635-649, December.
  9. Buch, A. & Dorfleitner, G., 2008. "Coherent risk measures, coherent capital allocations and the gradient allocation principle," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 235-242, February.
  10. J. Dhaene & R. J. A. Laeven & S. Vanduffel & G. Darkiewicz & M. J. Goovaerts, 2008. "Can a Coherent Risk Measure Be Too Subadditive?," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(2), pages 365-386.
  11. Dhaene, J. & Henrard, L. & Landsman, Z. & Vandendorpe, A. & Vanduffel, S., 2008. "Some results on the CTE-based capital allocation rule," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 855-863, April.
  12. Bolancé, Catalina & Guillén, Montserrat & Nielsen, Jens Perch, 2008. "Inverse beta transformation in kernel density estimation," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1757-1764, September.
  13. Song Chen, 2000. "Probability Density Function Estimation Using Gamma Kernels," Annals of the Institute of Statistical Mathematics, Springer, vol. 52(3), pages 471-480, September.
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