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Non-parametric Models for Univariate Claim Severity Distributions - an approach using R

Author

Listed:
  • Catalina Bolance

    (Department of Econometrics, Riskcenter-IREA, Universitat de Barcelona)

  • Montserrat Guillen

    (Department of Econometrics, Riskcenter-IREA, Universitat de Barcelona)

  • David Pitt

    (Department of Applied Finance and Actuarial Studies, Macquarie University)

Abstract

This paper presents an analysis of motor vehicle insurance claims relating to vehicle damage and to associated medical expenses. We use univariate severity distributions esti- mated with non-parametric methods. The methods are implemented using the statistical package R. The nonparametric analysis presented involves kernel density estimation. We illustrate the benefits of applying transformations to data prior to employing kernel based methods. We use a log-transformation and an optimal transformation amongst a class of transformations that produces symmetry in the data. The central aim of this paper is to provide educators with material that can be used in the classroom to teach statistical estimation methods, goodness of fit analysis and importantly statistical computing in the context of insurance and risk management. To this end, we have included in the Appendix of this paper all the R code that has been used in the analysis so that readers, both students and educators, can fully explore the techniques described.

Suggested Citation

  • 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.
    • Handle: RePEc:bak:wpaper:201401
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    File URL: http://www.ub.edu/rfa/research/WP/UBriskcenterWP201401.pdf
    File Function: First version, 2014
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    References listed on IDEAS

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    1. Marco Corazza & Florence Legros & Cira Perna & Marilena Sibillo, 2017. "Mathematical and Statistical Methods for Actuarial Sciences and Finance," Post-Print hal-01776135, HAL.
    2. Zhang, Xibin & King, Maxwell L. & Hyndman, Rob J., 2006. "A Bayesian approach to bandwidth selection for multivariate kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3009-3031, July.
    3. Jan Dhaene & Mark Goovaerts & Rob Kaas, 2003. "Economic Capital Allocation Derived from Risk Measures," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(2), pages 44-56.
    4. Bolance, Catalina & Guillen, Montserrat & Nielsen, Jens Perch, 2003. "Kernel density estimation of actuarial loss functions," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 19-36, February.
    5. Wu, Tiee-Jian & Chen, Ching-Fu & Chen, Huang-Yu, 2007. "A variable bandwidth selector in multivariate kernel density estimation," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 462-467, February.
    6. 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.
    7. Liu, Qing & Pitt, David & Zhang, Xibin & Wu, Xueyuan, 2011. "A Bayesian Approach to Parameter Estimation for Kernel Density Estimation via Transformations," Annals of Actuarial Science, Cambridge University Press, vol. 5(2), pages 181-193, September.
    8. Vernic, Raluca, 2006. "Multivariate skew-normal distributions with applications in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 413-426, April.
    9. Valdez, Emiliano A. & Chernih, Andrew, 2003. "Wang's capital allocation formula for elliptically contoured distributions," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 517-532, December.
    10. Hall, Peter & Marron, J. S., 1987. "Estimation of integrated squared density derivatives," Statistics & Probability Letters, Elsevier, vol. 6(2), pages 109-115, November.
    11. 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.
    12. Clements A. & Hurn S. & Lindsay K., 2003. "Mobius-Like Mappings and Their Use in Kernel Density Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 993-1000, January.
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    Cited by:

    1. 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.
    2. Manuela Alcañiz & Aïda Solé-Auró, 2018. "Ageing and health-related quality of life: evidence from Catalonia (Spain)," Working Papers 2018-01, Universitat de Barcelona, UB Riskcenter.
    3. Estefanía Alaminos & Mercedes Ayuso, 2015. "Methodological Approach of a Multiple State Actuarial Model for the Married - Widower case for the assessment of retirement and widowhood pensions," Working Papers 2015-04, Universitat de Barcelona, UB Riskcenter.
    4. Xavier Piulachs & Ramon Alemany & Montserrat Guillen, 2014. "A joint longitudinal and survival model with health care usage for insured elderly," Working Papers 2014-07, Universitat de Barcelona, UB Riskcenter.

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    Loss modeling; insurance; finance;
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