Skip to main content

Machine learning techniques for mortality modeling

Abstract

Various stochastic models have been proposed to estimate mortality rates. In this paper we illustrate how machine learning techniques allow us to analyze the quality of such mortality models. In addition, we present how these techniques can be used for differentiating the different causes of death in mortality modeling.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

References

  1. Alai DH, Arnold S, Sherris M (2015) Modelling cause-of-death mortality and the impact of cause-elimination. Ann Actuar Sci 9(1):167–186

    Article  Google Scholar 

  2. Breiman L, Friedman J, Olshen RA, Stone CJ (1984) Classification and regression trees. Wadsworth Statistics/Probability Series, Chapman and Hall/CRC, Boca Raton

    MATH  Google Scholar 

  3. Cairns AJG, Blake D, Dowd K, Coughlan GD, Epstein D, Ong A, Balevich I (2009) A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. N Am Actuar J 13(1):1–35

    MathSciNet  Article  Google Scholar 

  4. Hirz J, Schmock U, Shevchenko P (2017) Actuarial Applications and Estimation of extended CreditRisk+. Risks 5(2):23

    Article  Google Scholar 

  5. Lee RD, Carter LR (1992) Modeling and forecasting U.S. mortality. J Am Stat Assoc 87(419):659–671

    MATH  Google Scholar 

  6. Renshaw AE, Haberman S (2003) Lee–Carter mortality forecasting: a parallel generalized linear modelling approach for England and Wales mortality projections. J R Stat Soc Ser C (Appl Stat) 52(1):119–137

    MathSciNet  Article  MATH  Google Scholar 

  7. Renshaw AE, Haberman S (2006) A cohort-based extension to the Lee–Carter model for mortality reduction factors. Insur Math Econ 38(3):556–570

    Article  MATH  Google Scholar 

  8. Richards SJ (2009) Selected issues in modelling mortality by cause and in small populations. Br Actuar J 15(supplement):267–283

    Article  Google Scholar 

  9. Stommel H, Stommel E (1983) Volcano weather: the story of 1816, the year without a summer. Seven Seas Press, Newport

    MATH  Google Scholar 

  10. Therneau TM, Atkinson EJ (2015) An introduction to recursive partitioning using the RPART routines. R Vignettes. Mayo Foundation, Rochester

    Google Scholar 

  11. Villegas AM, Millossovich P, Kaishev V (2016) StMoMo: an R package for stochastic mortality modelling. R Vignettes

  12. Wüthrich MV (2016) Non-life insurance: mathematics & statistics. https://ssrn.com/abstract=2319328

  13. Wüthrich MV, Buser C (2016) Data analytics for non-life insurance pricing. https://ssrn.com/abstract=2870308

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Philippe Deprez.

Appendix

Appendix

Figures on Swiss cause-of-death mortality

See Figs. 5, 6, 7, and 8.

Fig. 5
figure 5

The odd rows illustrate the regression tree estimated probabilities \(\theta ^ {\rm tree}(k| {\varvec{x}})\) for females. These plots all have the same scale given in the middle plot in each odd row. The even rows show the corresponding Pearson’s residuals given by (8). These plots all have the same scale given in the middle plot in each even row

Fig. 6
figure 6

The odd rows illustrate the regression tree estimated probabilities \(\theta ^ {\rm tree}(k| {\varvec{x}})\) for males. These plots all have the same scale given in the middle plot in each odd row. The even rows show the corresponding Pearson’s residuals given by (8). These plots all have the same scale given in the middle plot in each even row

Fig. 7
figure 7

Regression tree estimated probabilities \(\theta ^ {\rm tree}(k| {\varvec{x}})\) for females and for the 12 different causes of death considered

Fig. 8
figure 8

Regression tree estimated probabilities \(\theta ^ {\rm tree}(k| {\varvec{x}})\) for males and for the 12 different causes of death considered

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Deprez, P., Shevchenko, P.V. & Wüthrich, M.V. Machine learning techniques for mortality modeling. Eur. Actuar. J. 7, 337–352 (2017). https://doi.org/10.1007/s13385-017-0152-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13385-017-0152-4

Keywords

  • Mortality modeling
  • Cause-of-death mortality
  • Machine learning
  • Boosting
  • Regression