Skip to main content

Comonotonic Approximations to Quantiles of Life Annuity Conditional Expected Present Values: Extensions to General Arima Models and Comparison with the Bootstrap

  • M. Denuit (a1), S. Haberman (a2) and A.E. Renshaw (a3)

This paper aims to provide accurate approximations for the quantiles of the conditional expected present value of the payments made by the annuity provider, given the future path of the Lee-Carter time index. Conditional cohort and period life expectancies are also considered. The paper also addresses some associated simulation issues, which, hitherto, have been unresolved.

Hide All
Brockwell P.J. and Davis R.A. (2002) Introduction to Time Series and Forecasting. Springer.
Brouhns N., Denuit M. and Vermunt J.K. (2002) Measuring the longevity risk in mortality projections. Bulletin of the Swiss Association of Actuaries, 105130.
Cairns A.J.G., Blake D. and Dowd K. (2006) A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration. Journal of Risk and Insurance 73, 687718.
Denuit M. (2007) Distribution of the random future life expectancies in log-bilinear mortality projection models. Lifetime Data Analysis, 13, 381397.
Denuit M. and Dhaene J. (2007) Comonotonic bounds on the survival probabilities in the Lee-Carter model for mortality projection. Computational and Applied Mathematics 203, 169176.
Denuit M. and Vermandele C. (1998) Optimal reinsurance and stop-loss order. Insurance: Mathematics and Economics 22, 229233.
Haberman S. and Renshaw A.E. (2009) On age-period-cohort parametric mortality rate projections. Insurance: Mathematics and Economics, 45, 255270.
Hamilton J.D. (1994) Time Series Analysis. Princeton University Press, Princeton, New-Jersey.
Lee R.D. and Carter L. (1992) Modelling and forecasting the time series of US mortality. Journal of the American Statistical Association (with discussion) 87, 659671.
Plat R. (2009) On stochastic mortality modeling. Insurance: Mathematics and Economics, 45, 393404.
Renshaw A.E. and Haberman S. (2003) Lee-Carter mortality forecasting with age-specific enhancement. Insurance: Mathematics and Economics, 33, 255272.
Renshaw A.E. and Haberman S. (2006) A cohort based extension to the Lee-Carter model for mortality reduction factors. Insurance: Mathematics and Economics, 38, 556570.
Renshaw A.E. and Haberman S. (2008) On simulation based approaches to risk measurement in mortality with specific reference to Poisson Lee-Carter. Insurance: Mathematics and Economics, 42, 797816.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

ASTIN Bulletin: The Journal of the IAA
  • ISSN: 0515-0361
  • EISSN: 1783-1350
  • URL: /core/journals/astin-bulletin-journal-of-the-iaa
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 21 *
Loading metrics...

Abstract views

Total abstract views: 103 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 24th January 2018. This data will be updated every 24 hours.