Skip to main content

Advertisement

SpringerLink
Log in

A user-friendly approach to stochastic mortality modelling

  • Original Research Paper
  • Published:
European Actuarial Journal Aims and scope Submit manuscript

Abstract

This paper proposes a general approach to stochastic mortality modelling. The logit transforms of annual survival probabilities are modelled by a linear combination of user-specified basis function of age. The model is easy to calibrate using the maximum likelihood method. The flexible construction and tangible interpretation of the underlying risk factors allows for an easy incorporation of population-specific characteristics and user views into the model. We fit two versions of the model into Finnish adult (18–100 years) population and mortality data, and present simulations for the future development of life spans.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

Notes

  1. University of California, Berkeley (USA) and Max Planck Institute for Demographic Research (Germany); http://www.mortality.org.

References

  1. Alho JM, Hougaard Jensen S, Lassila J (eds) (2008) Uncertain demographics and fiscal sustainability. Cambridge University Press, New York

    Google Scholar 

  2. Alho JM, Spencer BD (2005) Statistical demography and forecasting. Springer, New York

    MATH  Google Scholar 

  3. Aro H, Pennanen T (2011) Stochastic modelling of mortality and financial markets (manuscript)

  4. Ben-Tal A, Nemirovski A (2001) Lectures on modern convex optimization: analysis, algorithms, and engineering applications: analysis, algorithms, and engineering applications. MPS/SIAM series on optimization. Society for Industrial and Applied Mathematics (SIAM), Philadelphia

  5. Biffis E, Blake D (2009) Mortality-linked securities and derivatives. Pensions Institute discussion paper, PI 0901

  6. Blake D, Cairns AJG, Dowd K (2006) Living with mortality: longevity bonds and other mortality-linked securities. Br Actuar J 12(45):153–197

    Google Scholar 

  7. Booth H, Maindonald J, Smith L (2002) Applying Lee-Carter under conditions of variable mortality decline. Popul Stud 56(3):325–336

    Article  Google Scholar 

  8. Brouhns N, Denuit M, Vermunt J (2002) A Poisson log-bilinear regression approach to the construction of projected lifetables. Insur Math Econ 31(3):373–393

    Article  MathSciNet  MATH  Google Scholar 

  9. Cairns A (2000) A discussion of parameter and model uncertainty in insurance. Insur Math Econ 27:313–330

    Article  MATH  Google Scholar 

  10. Cairns AJG, Blake D, Dowd K (2006) A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration. J Risk Insur 73(4):687–718

    Article  Google Scholar 

  11. Cairns AJG, Blake D, Dowd K (2008) Modelling and management of mortality risk: a review. Scand Actuar J 2(3):79–113

    Article  MathSciNet  Google Scholar 

  12. Cairns AJG, Blake D, Dowd K, Coughlan GD, Epstein D, Ong A, Balevich I (2007) A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. Pensions Institute discussion paper, PI 0701

  13. Currie ID, Durban M, Eilers PHC (2004) Smoothing and forecasting mortality rates. Stat Model Int J 4(4):279–298

    Article  MathSciNet  MATH  Google Scholar 

  14. Dahl M (2004) Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts. Insur Math Econ 35(1):113–136

    Article  MathSciNet  MATH  Google Scholar 

  15. Dahl M, Moller T (2006) Valuation and hedging of life insurance liabilities with systematic mortality risk. Insur Math Econ 39(2):193–217

    Article  MathSciNet  MATH  Google Scholar 

  16. De Jong P, Tickle L (2006) Extending the Lee-Carter model of mortality projection. Math Popul Stud 13:1–18

    Article  MathSciNet  MATH  Google Scholar 

  17. Delwarde A, Denuit M, Eilers P (2007) Smoothing the Lee-Carter and Poisson log-bilinear models for mortality forecasting: a penalised log-likelihood approach. Stat Model 7:29–48

    Article  MathSciNet  Google Scholar 

  18. Dowd K, Blake D, Cairns AJG, Dawson P (2006) Survivor swaps. J Risk Insur 73(1):1–17

    Article  Google Scholar 

  19. Hilli P, Koivu M, Pennanen T (2011) Cash-flow based valuation of pension liabilities. Eur Actuar J (this issue)

  20. Hilli P, Koivu M, Pennanen T (2011) Optimal construction of a fund of funds. Eur Actuar J (this issue)

  21. Lee R, Carter L (1992) Modeling and forecasting U.S. mortality. J Am Stat Assoc 87(419):659–671

    Article  Google Scholar 

  22. Lee R, Miller T (2001) Evaluating the performance of the Lee-Carter method for forecasting mortality. Demography 38(4):537–549

    Article  Google Scholar 

  23. Lin Y, Cox SH (2005) Securitization of mortality risks in life annuities. J Risk Insur 72(2):227–252

    Article  Google Scholar 

  24. Milevsky MA, Promislow SD (2001) Mortality derivatives and the option to annuitise. Insur Math Econ 29(3):299–318 (papers presented at the 4th IME conference, Universitat de Barcelona, Barcelona, 24–26 July)

    Google Scholar 

  25. Nesterov Yu (2004) Introductory lectures on convex optimization: a basic course. In: Applied optimization, vol 87. Kluwer, Boston

  26. Renshaw AE, Haberman S (2003) Lee-Carter mortality forecasting with age-specific enhancement. Insur Math Econ 33(2):255–272

    Article  MathSciNet  MATH  Google Scholar 

  27. 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 

  28. Rockafellar RT, Wets RJ-B (1998) Variational analysis. Grundlehren der Mathematischen Wissenschaften (Fundamental Principles of Mathematical Sciences), vol 317. Springer, Berlin

  29. Schwartz G (1978) Estimating the dimension of a model. Ann Stat 6(2):461–464

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Systems Analysis, Aalto University, Helsinki, Finland

    Helena Aro

  2. Department of Mathematics and Statistics, University of Jyväskylä, Jyväskylä, Finland

    Teemu Pennanen

Authors
  1. Helena Aro
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Teemu Pennanen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Helena Aro.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aro, H., Pennanen, T. A user-friendly approach to stochastic mortality modelling. Eur. Actuar. J. 1 (Suppl 2), 151–167 (2011). https://doi.org/10.1007/s13385-011-0030-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13385-011-0030-4

Keywords

Search

Navigation