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A DOUBLE COMMON FACTOR MODEL FOR MORTALITY PROJECTION USING BEST-PERFORMANCE MORTALITY RATES AS REFERENCE

Published online by Cambridge University Press:  01 February 2021

Jackie Li ,
Maggie Lee  and
Simon Guthrie
Jackie Li*
Affiliation:
Department of Actuarial Studies and Business Analytics Macquarie University, Sydney, New South Wales 2109, Australia E-Mail: jackie.li@mq.edu.au
Maggie Lee
Affiliation:
Department of Actuarial Studies and Business Analytics Macquarie University, Sydney, New South Wales 2109, Australia E-Mail: maggie.lee@mq.edu.au
Simon Guthrie
Affiliation:
Department of Actuarial Studies and Business Analytics Macquarie University, Sydney, New South Wales 2109, Australia E-Mail: simon.guthrie@mq.edu.au
*
E-Mail: jackie.li@mq.edu.au
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Abstract

We construct a double common factor model for projecting the mortality of a population using as a reference the minimum death rate at each age among a large number of countries. In particular, the female and male minimum death rates, described as best-performance or best-practice rates, are first modelled by a common factor model structure with both common and sex-specific parameters. The differences between the death rates of the population under study and the best-performance rates are then modelled by another common factor model structure. An important result of using our proposed model is that the projected death rates of the population being considered are coherent with the projected best-performance rates in the long term, the latter of which serves as a very useful reference for the projection based on the collective experience of multiple countries. Our out-of-sample analysis shows that the new model has potential to outperform some conventional approaches in mortality projection.

Keywords

Common factor modelbest-performance/best-practice life expectancygeneralised extreme value distribution for minimacoherent mortality projectionG22J11C38
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 51 , Issue 2 , May 2021 , pp. 349 - 374
Copyright
© 2021 by Astin Bulletin. All rights reserved

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References

Biffis, E., Lin, Y. and Milidonis, A. (2017) The cross-section of Asia-Pacific mortality dynamics: implications for longevity risk sharing. Journal of Risk and Insurance, 84(S1), 515–532.CrossRefGoogle Scholar
Brouhns, N., Denuit, M. and Vermunt, J.K. (2002) A Poisson log-bilinear regression approach to the construction of projected lifetables. Insurance: Mathematics and Economics, 31, 373–393.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(4), 687–718.CrossRefGoogle Scholar
Cairns, A.J.G., Blake, D., Dowd, K., Coughlan, G.D., Epstein, D., Ong, A. and Balevich, I. (2009) A quantitative comparison of stochastic mortality models using data from England Wales and the United States. North American Actuarial Journal, 13(1), 1–35.CrossRefGoogle Scholar
Canudas-Romo, V., Booth, H. and Bergeron-Boucher, M.P. (2019) Minimum death rates and maximum life expectancy: The role of concordant ages. North American Actuarial Journal, 23(3), 322–334.CrossRefGoogle Scholar
Chen, R.Y. and Millossovich, P. (2018) Sex-specific mortality forecasting for UK countries: A coherent approach. European Actuarial Journal, 8, 69–95.CrossRefGoogle ScholarPubMed
Enchev, V., Kleinow, T. and Cairns, A.J.G. (2017) Multi-population mortality models: Fitting, forecasting and comparisons. Scandinavian Actuarial Journal, 2017(4), 319–342.CrossRefGoogle Scholar
Haberman, S., Kaishev, V., Millossovich, P., Villegas, A., Baxter, S., Gaches, A., Gunnlaugsson, S. and Sison, M. (2014) Longevity Basis Risk: A Methodology for Assessing Basis Risk. London, UK: Cass Business School and Hymans Robertson LLP, Institute and Faculty of Actuaries (IFoA) and Life and Longevity Markets Association (LLMA).Google Scholar
Haberman, S. and Renshaw, A. (2011) A comparative study of parametric mortality projection models. Insurance: Mathematics and Economics, 48, 35–55.Google Scholar
Human Mortality Database (HMD). (2020) University of California, Berkeley (USA) and Max Planck Institute for Demographic Research (Germany). www.mortality.org Google Scholar
Lee, R. (2000) The Lee-Carter method for forecasting mortality, with various extensions and applications. North American Actuarial Journal, 4(1), 80–93.CrossRefGoogle Scholar
Lee, R. and Carter, L. (1992) Modeling and forecasting U.S. mortality. Journal of the American Statistical Association, 87(419), 659–671.Google Scholar
Lee, R. and Miller, T. (2001) Evaluating the performance of the Lee-Carter method for forecasting mortality. Demography, 38(4), 537–549.CrossRefGoogle ScholarPubMed
Li, J. (2013) A Poisson common factor model for projecting mortality and life expectancy jointly for females and males. Population Studies, 67(1), 111–126.CrossRefGoogle ScholarPubMed
Li, J. and Haberman, S. (2015) On the effectiveness of natural hedging for insurance companies and pension plans. Insurance: Mathematics and Economics, 61, 286–297.Google Scholar
Li, J., Tickle, L. and Parr, N. (2016) A multi-population evaluation of the Poisson common factor model for projecting mortality jointly for both sexes. Journal of Population Research, 33(4), 333–360.CrossRefGoogle Scholar
Li, J.S.H. and Hardy, M.R. (2011) Measuring basis risk in longevity hedges. North American Actuarial Journal, 15(2), 177–200.CrossRefGoogle Scholar
Li, J.S.H. and Luo, A. (2012) Key q-duration: A framework for hedging longevity risk. ASTIN Bulletin, 42(2), 413–452.Google Scholar
Li, J.S.H., Zhou, R. and Hardy, M. (2015) A step-by-step guide to building two-population stochastic mortality models. Insurance: Mathematics and Economics, 63, 121–134.Google Scholar
Li, N. and Lee, R. (2005) Coherent mortality forecasts for a group of populations: An extension of the Lee-Carter method. Demography, 42(3), 575–594.CrossRefGoogle ScholarPubMed
Li, N., Lee, R. and Tuljapurkar, S. (2004) Using the Lee-Carter method to forecast mortality for populations with limited data. International Statistical Review, 72(1), 19–36.CrossRefGoogle Scholar
Lin, T. and Tsai, C.C.L. (2016) Hedging mortality/longevity risks of insurance portfolios for life insurer/annuity provider and financial intermediary. Insurance: Mathematics and Economics, 66, 44–58.Google Scholar
Liu, J. and Li, J. (2019) Beyond the highest life expectancy: Construction of proxy upper and lower life expectancy bounds. Journal of Population Research, 36(2), 159–181.CrossRefGoogle Scholar
Oeppen, J. and Vaupel, J.W. (2002) Broken limits to life expectancy. Science, 296(5570), 1029–1031.CrossRefGoogle ScholarPubMed
Parr, N., Li, J. and Tickle, L. (2016) A cost of living longer: Projections of the effects of prospective mortality improvement on economic support ratios for 14 advanced economies. Population Studies, 70(2), 181–200.CrossRefGoogle ScholarPubMed
Pitt, D., Li, J. and Lim, T.K. (2018) Smoothing Poisson common factor model for projecting mortality jointly for both sexes. ASTIN Bulletin, 48(2), 509–541.CrossRefGoogle 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
Vallin, J. and Meslé, F. (2008) Minimum mortality: A predictor of future progress? Population, 63, 557–590.CrossRefGoogle Scholar
Villegas, A.M., Haberman, S., Kaishev, V.K. and Millossovich, P. (2017a) A comparative study of two-population models for the assessment of basis risk in longevity hedges. ASTIN Bulletin, 47(3), 631–679.CrossRefGoogle Scholar
Villegas, A.M., Millossovich, P. and Kaishev, V.K. (2017b) StMoMo: An R package for stochastic mortality modeling. https://cran.r-project.org/web/packages/StMoMo/vignettes/StMoMoVignette.pdf CrossRefGoogle Scholar
Wilson, C. (2011) Understanding global demographic convergence since 1950. Population and Development Review, 37(2), 375–388.CrossRefGoogle Scholar
Wong, K., Li, J. and Tang, S. (2020) A modified common factor model for modelling mortality jointly for both sexes. Journal of Population Research. https://link.springer.com/article/10.1007/s12546-020-09243-zCrossRefGoogle Scholar
Yang, B., Li, J. and Balasooriya, U. (2016) Cohort extensions of the Poisson common factor model for modelling both genders jointly. Scandinavian Actuarial Journal, 2016(2), 93–112.CrossRefGoogle Scholar
Zhou, K.Q. and Li, J.S.H. (2017) Dynamic longevity hedging in the presence of population basis risk: A feasibility analysis from technical and economic perspectives. Journal of Risk and Insurance, 84(S1), 417–437.CrossRefGoogle Scholar