Skip to main content

Approximations for quantiles of life expectancy and annuity values using the parametric improvement rate approach to modelling and projecting mortality

European Actuarial Journal volume 3, pages 191–201 (2013)Cite this article

Abstract

In this paper, we develop accurate approximations for medians of life expectancy and life annuity pure premiums viewed as functions of future mortality trends as predicted by parametric models of the improvement rates in mortality. Numerical illustrations show that the comonotonic approximations perform well in this case, which suggests that they can be used in practice to evaluate the consequences of the uncertainty in future death rates. Prediction intervals based on 5 and 95 % quantiles are also considered but appear to be wider compared to simulated ones. This provides the practitioner with a conservative shortcut, thereby avoiding the problem of simulations within simulations in, for instance, Solvency 2 calculations.

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

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

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

Fig. 1

References

  1. Brouhns N, Denuit M, Vermunt JK (2002) A Poisson log-bilinear approach to the construction of projected life tables. Insur Math Econ 31:373–393

    Article  MathSciNet  MATH  Google Scholar 

  2. Denuit M (2007) Distribution of the random future life expectancies in log-bilinear mortality projection models. Lifetime Data Anal 13:381–397

    Article  MathSciNet  MATH  Google Scholar 

  3. Denuit M, Dhaene J (2007) Comonotonic bounds on the survival probabilities in the Lee-Carter model for mortality projection. Comput Appl Math 203:169–176

    MathSciNet  MATH  Google Scholar 

  4. Denuit M, Dhaene J, Goovaerts MJ, Kaas R (2005) Actuarial theory for dependent risks: measures, orders and models. Wiley, New York

    Book  Google Scholar 

  5. Denuit M, Haberman S, Renshaw AE (2010) Comonotonic approximations to quantiles of life annuity conditional expected present values: extensions to general ARIMA models and comparison with the bootstrap. ASTIN Bull 40:331–349

    Article  MathSciNet  MATH  Google Scholar 

  6. Haberman S, Renshaw AE (2012) Parametric mortality improvement rate modelling and projecting. Insur Math Econ 50:309–333

    Article  MathSciNet  MATH  Google Scholar 

  7. Lee RD, Carter L (1992) Modelling and forecasting the time series of US mortality. J Am Stat Assoc 87:659–675 (with discussion)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The authors would like to express their gratitude to an anonymous Referee whose comments have been extremely useful to revise a previous version of the present work. The financial support of PARC “Stochastic Modelling of Dependence” 2012–2017 awarded by the Communauté française de Belgique is gratefully acknowledged by Michel Denuit.

Author information

Authors and Affiliations

  1. Universite Catholique de Louvain, Louvain-la-Neuve, Belgium

    Michel Denuit

  2. Cass Business School, City University London, London, UK

    Steven Haberman & Arthur E. Renshaw

Authors
  1. Michel Denuit
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Steven Haberman
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Arthur E. Renshaw
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Steven Haberman.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Denuit, M., Haberman, S. & Renshaw, A.E. Approximations for quantiles of life expectancy and annuity values using the parametric improvement rate approach to modelling and projecting mortality. Eur. Actuar. J. 3, 191–201 (2013). https://doi.org/10.1007/s13385-013-0065-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13385-013-0065-9

Keywords

  • Life annuity
  • Life expectancy
  • Mortality projection
  • Comonotonicity
  • Simulation