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Risk classification in life insurance: methodology and case study

European Actuarial Journal volume 1, pages 23–41 (2011)Cite this article

Abstract

In this paper, we describe how Poisson regression analysis can be efficiently used to perform graduation of mortality rates in presence of exogenous information supporting an efficient underwriting process in life insurance business. After having justified the relevance of a Poisson likelihood for mortality data, we explain how categorical and continuous covariates can be included in the model. A case study based on a German insurance portfolio is proposed to illustrate the usefulness of the approach described in this paper.

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References

  1. Brown RL, McDaid J (2003) Factors affecting retirement mortality. N Am Actuar J 7(2):24–43

    MATH  MathSciNet  Google Scholar 

  2. Cossette H, Delwarde A, Denuit M, Guillot F, Marceau E (2007) Pension plan valuation and dynamic mortality tables. N Am Actuar J 11(2):1–34

    MathSciNet  Google Scholar 

  3. DAV (2008) Herleitung der Sterbetafel DAV 2008 T für Lebensversicherungen mit Todesfallcharakter. DAV-Unterarbeitsgruppe Todesfallrisiko. Blätter der DGVFM 30(1):189–224

  4. De Jong P, Heller GZ (2008) Generalized linear models for insurance data. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  5. England PD, Haberman S (1993) A new approach to modeling excess mortality. J Actuar Pract 1:85–117

    MATH  Google Scholar 

  6. Fahrmeir L, Tutz G (2001) Multivariate statistical modelling based on generalized linear models. Springer series in statistics, 2nd edn. Springer, New York

    Google Scholar 

  7. Gerber HU (1997) Life insurance mathematics, 3rd edn. Springer, Berlin

    MATH  Google Scholar 

  8. Haberman S, Renshaw AE (1990) Generalised linear models and excess mortality from peptic ulcers. Insur Math Econ 9(1):21–32

    Article  MathSciNet  Google Scholar 

  9. Haberman S, Renshaw AE (1996) Generalized linear models and actuarial science. The Statistician 45(4):407–436

    Article  Google Scholar 

  10. Laird NM, Olivier D (1981) Covariance analysis of censored survival data using log-linear analysis techniques. J Am Stat Assoc 76:231–240

    Article  MATH  MathSciNet  Google Scholar 

  11. Loader C (1999) Local regression and likelihood. Statistics and computing series. Springer, New York

    Google Scholar 

  12. Loader C (2010) locfit : local regression, likelihood and density estimation. R package version 1.5-6. http://cran.r-project.org/package=locfit

  13. McCullagh P, Nelder JA (1989) Generalized linear models. Monographs on statistics and applied probability, vol 37, 2nd edn. Chapman & Hall/CRC Press, Boca Raton

  14. R Development Core Team (2011) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. http://www.r-project.org.

  15. Regenauer A (2001) Kein Interesse am gläsernen Patient. Deutsches Ärzteblatt 98(10):A593–A596

    Google Scholar 

  16. Renshaw AE (1988) Modelling excess mortality using GLIM. J Inst Actuar 115:299–315

    Google Scholar 

  17. Renshaw AE (1991) Actuarial graduation practice and generalized linear and non-linear models. J Inst Actuar 118:295–312

    Google Scholar 

  18. Renshaw AE, Haberman S (1996) Dual modelling and select mortality. Insur Math Econ 19(2):105–126

    Article  Google Scholar 

  19. Renshaw AE, Haberman S, Hatzopoulos P(1997) On the duality of assumptions underpinning the construction of life tables. ASTIN Bull 27(1):5–22

    Article  Google Scholar 

  20. Sijbrands EJG, Tornij E, Homsma SJ (2009) Mortality risk prediction by an insurance company and long-term follow-up of 62,000 men. PLoS ONE 4(5):e5457

    Article  Google Scholar 

  21. Vinsonhaler C, Ravishanker N, Vadiveloo J, Rasoanaivo G (2001) Multivariate analysis of pension plan mortality data. N Am Actuar J 5(2):126–138

    MATH  MathSciNet  Google Scholar 

  22. Von Gaudecker H-M, Scholz RD (2007) Differential mortality by lifetime earnings in Germany. Demogr Res 17:83–108

    Article  Google Scholar 

  23. Wood SN (2006) Generalized additive models—an introduction with R. Texts in statistical science series. Chapman & Hall/CRC Press, Boca Raton

    Google Scholar 

  24. Wood SN (2011) mgcv : GAMs with GCV/AIC/REML smoothness estimation and GAMMs by PQL. R package version 1.7-5. http://cran.r-project.org/package=mgcv

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Acknowledgments

The authors would like to thank an anonymous reviewer whose suggestions improved the original manuscript. The data analysis in this paper was performed with R , statistical software which is released under the GNU General Public License (GPL). For more information on R , the interested reader is referred to R Development Core Team [14]. Beyond the R code we conceived ourselves, we benefitted in particular from the locfit package, described in Loader [12].

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Authors and Affiliations

  1. Munich Reinsurance Company, Divisional Unit: Life, Munich, Germany

    Susanne Gschlössl & Pascal Schoenmaekers

  2. Institut de statistique, biostatistique et sciences actuarielles (ISBA), Université Catholique de Louvain, Louvain-la-Neuve, Belgium

    Michel Denuit

Authors
  1. Susanne Gschlössl
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  2. Pascal Schoenmaekers
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  3. Michel Denuit
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Corresponding author

Correspondence to Michel Denuit.

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Gschlössl, S., Schoenmaekers, P. & Denuit, M. Risk classification in life insurance: methodology and case study. Eur. Actuar. J. 1, 23–41 (2011). https://doi.org/10.1007/s13385-011-0028-y

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  • DOI: https://doi.org/10.1007/s13385-011-0028-y

Keywords

  • Life Table
  • Poisson Regression
  • Product Type
  • Life Insurance
  • Smoothing Window