Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-17T23:20:35.871Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  09 August 2013

M. Denuit ,
S. Haberman  and
A.E. Renshaw
M. Denuit
Affiliation:
Institut de statistique, biostatistique et sciences actuarielles (ISBA), Université catholique de Louvain (UCL), Louvain-la-Neuve, Belgium
S. Haberman
Affiliation:
Cass Business School, City University, London, United Kingdom
A.E. Renshaw
Affiliation:
Cass Business School, City University, London, United Kingdom
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Keywords

Life annuitylife expectancymortality projectionLee-Carter modelcomonotonicitysimulation
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 40 , Issue 1 , May 2010 , pp. 331 - 349
Copyright
Copyright © International Actuarial Association 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Brockwell, P.J. and Davis, R.A. (2002) Introduction to Time Series and Forecasting. Springer.Google Scholar
Brouhns, N., Denuit, M. and Vermunt, J.K. (2002) Measuring the longevity risk in mortality projections. Bulletin of the Swiss Association of Actuaries, 105–130.Google Scholar
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, 687–718.Google Scholar
Denuit, M. (2007) Distribution of the random future life expectancies in log-bilinear mortality projection models. Lifetime Data Analysis, 13, 381–397.Google Scholar
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, 169–176.Google Scholar
Denuit, M. and Vermandele, C. (1998) Optimal reinsurance and stop-loss order. Insurance: Mathematics and Economics 22, 229–233.Google Scholar
Haberman, S. and Renshaw, A.E. (2009) On age-period-cohort parametric mortality rate projections. Insurance: Mathematics and Economics, 45, 255–270.Google Scholar
Hamilton, J.D. (1994) Time Series Analysis. Princeton University Press, Princeton, New-Jersey.Google Scholar
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, 659–671.Google Scholar
Plat, R. (2009) On stochastic mortality modeling. Insurance: Mathematics and Economics, 45, 393–404.Google Scholar
Renshaw, A.E. and Haberman, S. (2003) Lee-Carter mortality forecasting with age-specific enhancement. Insurance: Mathematics and Economics, 33, 255–272.Google Scholar
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, 556–570.Google Scholar
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, 797–816.Google Scholar