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Skewed bivariate models and nonparametric estimation for the CTE risk measure

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

Abstract

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.

Suggested Citation

  • Bolance, Catalina & Guillen, Montserrat & Pelican, Elena & Vernic, Raluca, 2008. "Skewed bivariate models and nonparametric estimation for the CTE risk measure," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 386-393, December.
  • Handle: RePEc:eee:insuma:v:43:y:2008:i:3:p:386-393
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Catalina Bolance & Montserrat Guillen & David Pitt, 2014. "Non-parametric Models for Univariate Claim Severity Distributions - an approach using R," Working Papers 2014-01, Universitat de Barcelona, UB Riskcenter.
    2. Bolancé, Catalina & Bahraoui, Zuhair & Artís, Manuel, 2014. "Quantifying the risk using copulae with nonparametric marginals," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 46-56.
    3. Alemany, Ramon & Bolancé, Catalina & Guillén, Montserrat, 2013. "A nonparametric approach to calculating value-at-risk," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 255-262.
    4. Belles-Sampera, Jaume & Guillen, Montserrat & Santolino, Miguel, 2016. "What attitudes to risk underlie distortion risk measure choices?," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 101-109.
    5. Ramon Alemany & Catalina Bolancé & Montserrat Guillén, 2012. "Nonparametric estimation of Value-at-Risk," Working Papers XREAP2012-19, Xarxa de Referència en Economia Aplicada (XREAP), revised Oct 2012.
    6. repec:eee:insuma:v:75:y:2017:i:c:p:126-136 is not listed on IDEAS
    7. Buch-Kromann, Tine & Guillén, Montserrat & Linton, Oliver & Nielsen, Jens Perch, 2011. "Multivariate density estimation using dimension reducing information and tail flattening transformations," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 99-110, January.
    8. Belles-Sampera, Jaume & Guillén, Montserrat & Santolino, Miguel, 2014. "GlueVaR risk measures in capital allocation applications," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 132-137.
    9. Eling, Martin, 2014. "Fitting asset returns to skewed distributions: Are the skew-normal and skew-student good models?," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 45-56.
    10. Bernardi, Mauro & Maruotti, Antonello & Petrella, Lea, 2012. "Skew mixture models for loss distributions: A Bayesian approach," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 617-623.
    11. David Pitt & Montserrat Guillén, 2010. "An introduction to parametric and non-parametric models for bivariate positive insurance claim severity distributions," Working Papers XREAP2010-03, Xarxa de Referència en Economia Aplicada (XREAP), revised Mar 2010.
    12. David Pitt & Montserrat Guillen & Catalina Bolancé, 2011. "Estimation of Parametric and Nonparametric Models for Univariate Claim Severity Distributions - an approach using R," Working Papers XREAP2011-06, Xarxa de Referència en Economia Aplicada (XREAP), revised Jun 2011.
    13. Ramon Alemany & Catalina Bolance & Montserrat Guillen, 2014. "Accounting for severity of risk when pricing insurance products," Working Papers 2014-05, Universitat de Barcelona, UB Riskcenter.
    14. Jaume Belles-Sampera & Montserrat Guillén & Miguel Santolino, 2013. "“The use of flexible quantile-based measures in risk assessment”," IREA Working Papers 201323, University of Barcelona, Research Institute of Applied Economics, revised Dec 2013.
    15. Guillen, Montserrat & Prieto, Faustino & Sarabia, José María, 2011. "Modelling losses and locating the tail with the Pareto Positive Stable distribution," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 454-461.
    16. Eling, Martin, 2012. "Fitting insurance claims to skewed distributions: Are the skew-normal and skew-student good models?," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 239-248.
    17. Ramon ALEMANY & Catalina BOLANCÉ & Montserrat GUILLÉN & Alemar E. PADILLA-BARRETO, 2016. "Combining Parametric And Non-Parametric Methods To Compute Value-At-Risk," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 50(4), pages 61-74.
    18. Jaume Belles-Sampera & Montserrat Guillén & Miguel Santolino, 2013. "“Beyond Value-at-Risk: GlueVaR Distortion Risk Measures”," IREA Working Papers 201302, University of Barcelona, Research Institute of Applied Economics, revised Feb 2013.

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