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Accounting for severity of risk when pricing insurance products

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Author Info

  • Ramon Alemany

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

  • Catalina Bolance

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

  • Montserrat Guillen

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

Abstract

We design a system for improving the calculation of the price to be charged for an insurance product. Standard pricing techniques generally take into account the expected severity of potential losses. However, the severity of a loss can be extremely high and the risk of a severe loss is not homogeneous for all policy holders. We argue that risk loadings should be based on risk evaluations that avoid too many model assumptions. We apply a nonparametric method and illustrate our contribution with a real problem in the area of motor insurance.

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File URL: http://www.ub.edu/riskcenter/research/WP/UBriskcenterWP201405.pdf
File Function: First version, 2014
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Bibliographic Info

Paper provided by Universitat de Barcelona, UB Riskcenter in its series Working Papers with number 2014-05.

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Length: 25 pages
Date of creation: Apr 2014
Date of revision:
Handle: RePEc:bak:wpaper:201405

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Related research

Keywords: quantile; value-at-risk; loss models; extremes;

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References

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  1. Patrick L. Brockett & Linda L. Golden & Montserrat Guillen & Jens Perch Nielsen & Jan Parner & Ana Maria Perez-Marin, 2008. "Survival Analysis of a Household Portfolio of Insurance Policies: How Much Time Do You Have to Stop Total Customer Defection?," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(3), pages 713-737.
  2. 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.
  3. Sarabia, José María & Guillén, Montserrat, 2008. "Joint modelling of the total amount and the number of claims by conditionals," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 466-473, December.
  4. Bolancé, Catalina & Guillén, Montserrat & Pinquet, Jean, 2008. "On the link between credibility and frequency premium," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 209-213, October.
  5. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  6. Jan W. H. Swanepoel & Francois C. Van Graan, 2005. "A New Kernel Distribution Function Estimator Based on a Non-parametric Transformation of the Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 32(4), pages 551-562.
  7. J. Pinquet & M. Guillén & C. Bolancé, 2000. "Long-range contagion in automobile insurance data : estimation and implications for experience rating," THEMA Working Papers 2000-43, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  8. Lopez, Olivier, 2012. "A generalization of the Kaplan–Meier estimator for analyzing bivariate mortality under right-censoring and left-truncation with applications in model-checking for survival copula models," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 505-516.
  9. Jianqing Fan & Juan Gu, 2003. "Semiparametric estimation of Value at Risk," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 261-290, December.
  10. 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.
  11. Bermúdez, Lluís & Karlis, Dimitris, 2011. "Bayesian multivariate Poisson models for insurance ratemaking," Insurance: Mathematics and Economics, Elsevier, vol. 48(2), pages 226-236, March.
  12. Jones, Bruce L. & Zitikis, Ricardas, 2007. "Risk measures, distortion parameters, and their empirical estimation," Insurance: Mathematics and Economics, Elsevier, vol. 41(2), pages 279-297, September.
  13. O. Scaillet, 2004. "Nonparametric Estimation and Sensitivity Analysis of Expected Shortfall," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 115-129.
  14. 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.
  15. Krätschmer, Volker & Zähle, Henryk, 2011. "Sensitivity of risk measures with respect to the normal approximation of total claim distributions," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 335-344.
  16. 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.
  17. C. Bolancé & M. Guillén & J. Pinquet, 2002. "Time-varying credibility for frequency risk models : Estimation and tests for autoregressive specifications on the random effects," THEMA Working Papers 2002-18, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  18. Cai, Zongwu & Wang, Xian, 2008. "Nonparametric estimation of conditional VaR and expected shortfall," Journal of Econometrics, Elsevier, vol. 147(1), pages 120-130, November.
  19. Kevin Dowd & David Blake, 2006. "After VaR: The Theory, Estimation, and Insurance Applications of Quantile-Based Risk Measures," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(2), pages 193-229.
  20. 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.
  21. Peng, Liang & Qi, Yongcheng & Wang, Ruodu & Yang, Jingping, 2012. "Jackknife empirical likelihood method for some risk measures and related quantities," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 142-150.
  22. Turan G. Bali & Panayiotis Theodossiou, 2008. "Risk Measurement Performance of Alternative Distribution Functions," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 75(2), pages 411-437.
  23. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
  24. 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.
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