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Incorporating crossed classification credibility into the Lee–Carter model for multi-population mortality data

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  • Bozikas, Apostolos
  • Pitselis, Georgios

Abstract

Recent developments in actuarial literature have shown that credibility theory can serve as an effective tool in mortality modelling, leading to accurate forecasts when applied to single or multi-population datasets. This paper presents a crossed classification credibility formulation of the Lee–Carter method particularly designed for multi-population mortality modelling. Differently from the standard Lee–Carter methodology, where the time index is assumed to follow an appropriate time series process, herein, future mortality dynamics are estimated under a crossed classification credibility framework, which models the interactions between various risk factors (e.g. genders, countries). The forecasting performances between the proposed model, the original Lee–Carter model and two multi-population Lee–Carter extensions are compared for both genders of multiple countries. Numerical results indicate that the proposed model produces more accurate forecasts than the Lee–Carter type models, as evaluated by the mean absolute percentage forecast error measure. Applications with life insurance and annuity products are also provided and a stochastic version of the proposed model is presented.

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  • Bozikas, Apostolos & Pitselis, Georgios, 2020. "Incorporating crossed classification credibility into the Lee–Carter model for multi-population mortality data," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 353-368.
    • Handle: RePEc:eee:insuma:v:93:y:2020:i:c:p:353-368
    DOI: 10.1016/j.insmatheco.2020.06.005
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    1. Cary Chi-Liang Tsai & Adelaide Di Wu, 2020. "Bühlmann Credibility-Based Approaches to Modeling Mortality Rates for Multiple Populations," North American Actuarial Journal, Taylor & Francis Journals, vol. 24(2), pages 290-315, April.
    2. Chen, Hua & MacMinn, Richard & Sun, Tao, 2015. "Multi-population mortality models: A factor copula approach," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 135-146.
    3. Hyndman, Rob J. & Khandakar, Yeasmin, 2008. "Automatic Time Series Forecasting: The forecast Package for R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i03).
    4. Schinzinger, Edo & Denuit, Michel M. & Christiansen, Marcus C., 2016. "A multivariate evolutionary credibility model for mortality improvement rates," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 70-81.
    5. Wan, Cheng & Bertschi, Ljudmila, 2015. "Swiss coherent mortality model as a basis for developing longevity de-risking solutions for Swiss pension funds: A practical approach," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 66-75.
    6. Schinzinger, Edo & Denuit, Michel & Christiansen, Marcus, 2016. "A multivariate evolutionary credibility model for mortality improvement rates," LIDAM Reprints ISBA 2016019, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Plat, Richard, 2009. "On stochastic mortality modeling," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 393-404, December.
    8. Wang, Hsin-Chung & Yue, Ching-Syang Jack & Chong, Chen-Tai, 2018. "Mortality models and longevity risk for small populations," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 351-359.
    9. Kleinow, Torsten, 2015. "A common age effect model for the mortality of multiple populations," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 147-152.
    10. Andrew J. G. Cairns & David Blake & Kevin Dowd, 2006. "A Two‐Factor Model for Stochastic Mortality with Parameter Uncertainty: Theory and Calibration," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(4), pages 687-718, December.
    11. Cary Chi-Liang Tsai & Tzuling Lin, 2017. "A Bühlmann Credibility Approach to Modeling Mortality Rates," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(2), pages 204-227, April.
    12. Tsai, Cary Chi-Liang & Wu, Adelaide Di, 2020. "Incorporating hierarchical credibility theory into modelling of multi-country mortality rates," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 37-54.
    13. Apostolos Bozikas & Georgios Pitselis, 2018. "An Empirical Study on Stochastic Mortality Modelling under the Age-Period-Cohort Framework: The Case of Greece with Applications to Insurance Pricing," Risks, MDPI, vol. 6(2), pages 1-34, April.
    14. Nan Li & Ronald Lee, 2005. "Coherent mortality forecasts for a group of populations: An extension of the lee-carter method," Demography, Springer;Population Association of America (PAA), vol. 42(3), pages 575-594, August.
    15. Chris Wilson, 2001. "On the Scale of Global Demographic Convergence 1950–2000," Population and Development Review, The Population Council, Inc., vol. 27(1), pages 155-171, March.
    16. Valeria D’Amato & Steven Haberman & Gabriella Piscopo & Maria Russolillo & Lorenzo Trapani, 2014. "Detecting Common Longevity Trends by a Multiple Population Approach," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(1), pages 139-149.
    17. Mitchell, Daniel & Brockett, Patrick & Mendoza-Arriaga, Rafael & Muthuraman, Kumar, 2013. "Modeling and forecasting mortality rates," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 275-285.
    18. Hatzopoulos, P. & Haberman, S., 2009. "A parameterized approach to modeling and forecasting mortality," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 103-123, February.
    19. Bauwelinckx, T. & Goovaerts, M. J., 1990. "On a multilevel hierarchical credibility algorithm," Insurance: Mathematics and Economics, Elsevier, vol. 9(2-3), pages 221-228, September.
    20. Apostolos Bozikas & Georgios Pitselis, 2019. "Credible Regression Approaches to Forecast Mortality for Populations with Limited Data," Risks, MDPI, vol. 7(1), pages 1-22, February.
    21. Renshaw, A.E. & Haberman, S., 2006. "A cohort-based extension to the Lee-Carter model for mortality reduction factors," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 556-570, June.
    22. Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, vol. 8(3), pages 393-411, November.
    23. Hardy, M.R. & Panjer, H.H., 1998. "A Credibility Approach to Mortality Risk," ASTIN Bulletin, Cambridge University Press, vol. 28(2), pages 269-283, November.
    24. Cairns, Andrew J.G. & Blake, David & Dowd, Kevin & Coughlan, Guy D. & Khalaf-Allah, Marwa, 2011. "Bayesian Stochastic Mortality Modelling for Two Populations," ASTIN Bulletin, Cambridge University Press, vol. 41(1), pages 29-59, May.
    25. Li, Johnny Siu-Hang & Zhou, Rui & Hardy, Mary, 2015. "A step-by-step guide to building two-population stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 121-134.
    26. Johnny Li & Mary Hardy, 2011. "Measuring Basis Risk in Longevity Hedges," North American Actuarial Journal, Taylor & Francis Journals, vol. 15(2), pages 177-200.
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