IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i9p1550-d411425.html
   My bibliography  Save this article

A Comparison of Forecasting Mortality Models Using Resampling Methods

Author

Listed:
  • David Atance

    (Departamento de Economía y Dirección de Empresas, Universidad de Alcalá, Pza. San Diego S/N, 28801 Alcalá de Henares, Spain
    These authors contributed equally to this work.)

  • Ana Debón

    (Centro de Gestión de la Calidad y del Cambio, Universitat Politècnica de València, Camino de Vera, S/N, 46022 Valencia, Spain
    These authors contributed equally to this work.)

  • Eliseo Navarro

    (Departamento de Economía y Dirección de Empresas, Universidad de Alcalá, Pza. San Diego S/N, 28801 Alcalá de Henares, Spain
    These authors contributed equally to this work.)

Abstract

The accuracy of the predictions of age-specific probabilities of death is an essential objective for the insurance industry since it dramatically affects the proper valuation of their products. Currently, it is crucial to be able to accurately calculate the age-specific probabilities of death over time since insurance companies’ profits and the social security of citizens depend on human survival; therefore, forecasting dynamic life tables could have significant economic and social implications. Quantitative tools such as resampling methods are required to assess the current and future states of mortality behavior. The insurance companies that manage these life tables are attempting to establish models for evaluating the risk of insurance products to develop a proactive approach instead of using traditional reactive schemes. The main objective of this paper is to compare three mortality models to predict dynamic life tables. By using the real data of European countries from the Human Mortality Database, this study has identified the best model in terms of the prediction ability for each sex and each European country. A comparison that uses cobweb graphs leads us to the conclusion that the best model is, in general, the Lee–Carter model. Additionally, we propose a procedure that can be applied to a life table database that allows us to choose the most appropriate model for any geographical area.

Suggested Citation

  • David Atance & Ana Debón & Eliseo Navarro, 2020. "A Comparison of Forecasting Mortality Models Using Resampling Methods," Mathematics, MDPI, vol. 8(9), pages 1-21, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1550-:d:411425
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/9/1550/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/9/1550/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Danesi, Ivan Luciano & Haberman, Steven & Millossovich, Pietro, 2015. "Forecasting mortality in subpopulations using Lee–Carter type models: A comparison," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 151-161.
    2. Bergmeir, Christoph & Hyndman, Rob J. & Koo, Bonsoo, 2018. "A note on the validity of cross-validation for evaluating autoregressive time series prediction," Computational Statistics & Data Analysis, Elsevier, vol. 120(C), pages 70-83.
    3. Koissi, Marie-Claire & Shapiro, Arnold F. & Hognas, Goran, 2006. "Evaluating and extending the Lee-Carter model for mortality forecasting: Bootstrap confidence interval," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 1-20, February.
    4. Susanna Levantesi & Virginia Pizzorusso, 2019. "Application of Machine Learning to Mortality Modeling and Forecasting," Risks, MDPI, vol. 7(1), pages 1-19, February.
    5. Andrew Cairns & David Blake & Kevin Dowd & Guy Coughlan & David Epstein & Alen Ong & Igor Balevich, 2009. "A Quantitative Comparison of Stochastic Mortality Models Using Data From England and Wales and the United States," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(1), pages 1-35.
    6. Heather Booth & Rob Hyndman & Leonie Tickle & Piet de Jong, 2006. "Lee-Carter mortality forecasting: a multi-country comparison of variants and extensions," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 15(9), pages 289-310.
    7. Plat, Richard, 2009. "On stochastic mortality modeling," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 393-404, December.
    8. Ahcan, Ales & Medved, Darko & Olivieri, Annamaria & Pitacco, Ermanno, 2014. "Forecasting mortality for small populations by mixing mortality data," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 12-27.
    9. Debón, A. & Montes, F. & Puig, F., 2008. "Modelling and forecasting mortality in Spain," European Journal of Operational Research, Elsevier, vol. 189(3), pages 624-637, September.
    10. Julianne Holt-Lunstad & Timothy B Smith & J Bradley Layton, 2010. "Social Relationships and Mortality Risk: A Meta-analytic Review," PLOS Medicine, Public Library of Science, vol. 7(7), pages 1-1, July.
    11. Xiaoming Liu & W. John Braun, 2010. "Investigating Mortality Uncertainty Using the Block Bootstrap," Journal of Probability and Statistics, Hindawi, vol. 2010, pages 1-15, January.
    12. 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.
    13. Hainaut, Donatien, 2018. "A Neural-Network Analyzer for Mortality Forecast," LIDAM Reprints ISBA 2018027, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    14. Yang, Sharon S. & Yue, Jack C. & Huang, Hong-Chih, 2010. "Modeling longevity risks using a principal component approach: A comparison with existing stochastic mortality models," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 254-270, February.
    15. Han Li & Colin O’Hare, 2019. "Mortality Forecasting: How Far Back Should We Look in Time?," Risks, MDPI, vol. 7(1), pages 1-15, February.
    16. 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.
    17. 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.
    18. Brouhns, Natacha & Denuit, Michel & Vermunt, Jeroen K., 2002. "A Poisson log-bilinear regression approach to the construction of projected lifetables," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 373-393, December.
    19. Haberman, Steven & Renshaw, Arthur, 2011. "A comparative study of parametric mortality projection models," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 35-55, January.
    20. Andrew Hunt & David Blake, 2014. "A General Procedure for Constructing Mortality Models," North American Actuarial Journal, Taylor & Francis Journals, vol. 18(1), pages 116-138.
    21. 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).
    22. Ronald Lee & Timothy Miller, 2001. "Evaluating the performance of the lee-carter method for forecasting mortality," Demography, Springer;Population Association of America (PAA), vol. 38(4), pages 537-549, November.
    23. Tashman, Leonard J., 2000. "Out-of-sample tests of forecasting accuracy: an analysis and review," International Journal of Forecasting, Elsevier, vol. 16(4), pages 437-450.
    24. Hunt, Andrew & Blake, David, 2020. "Identifiability in age/period/cohort mortality models," Annals of Actuarial Science, Cambridge University Press, vol. 14(2), pages 500-536, September.
    25. 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.
    26. Neves, César & Fernandes, Cristiano & Hoeltgebaum, Henrique, 2017. "Five different distributions for the Lee–Carter model of mortality forecasting: A comparison using GAS models," Insurance: Mathematics and Economics, Elsevier, vol. 75(C), pages 48-57.
    27. Debón, A. & Martínez-Ruiz, F. & Montes, F., 2010. "A geostatistical approach for dynamic life tables: The effect of mortality on remaining lifetime and annuities," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 327-336, December.
    28. D’Amato, Valeria & Haberman, Steven & Piscopo, Gabriella & Russolillo, Maria, 2012. "Modelling dependent data for longevity projections," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 694-701.
    29. Wolfgang Härdle & Joel Horowitz & Jens‐Peter Kreiss, 2003. "Bootstrap Methods for Time Series," International Statistical Review, International Statistical Institute, vol. 71(2), pages 435-459, August.
    30. Hainaut, Donatien, 2018. "A Neural-Network Analyzer For Mortality Forecast," ASTIN Bulletin, Cambridge University Press, vol. 48(2), pages 481-508, May.
    31. Debon, A. & Montes, F. & Mateu, J. & Porcu, E. & Bevilacqua, M., 2008. "Modelling residuals dependence in dynamic life tables: A geostatistical approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3128-3147, February.
    32. Renshaw, A. E. & Haberman, S., 2003. "Lee-Carter mortality forecasting with age-specific enhancement," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 255-272, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jaap Spreeuw & Iqbal Owadally & Muhammad Kashif, 2022. "Projecting Mortality Rates Using a Markov Chain," Mathematics, MDPI, vol. 10(7), pages 1-18, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Blake, David & Cairns, Andrew J.G., 2021. "Longevity risk and capital markets: The 2019-20 update," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 395-439.
    2. Blake, David & El Karoui, Nicole & Loisel, Stéphane & MacMinn, Richard, 2018. "Longevity risk and capital markets: The 2015–16 update," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 157-173.
    3. Basellini, Ugofilippo & Camarda, Carlo Giovanni & Booth, Heather, 2023. "Thirty years on: A review of the Lee–Carter method for forecasting mortality," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1033-1049.
    4. David Atance & Alejandro Balbás & Eliseo Navarro, 2020. "Constructing dynamic life tables with a single-factor model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 787-825, December.
    5. Basellini, Ugofilippo & Camarda, Carlo Giovanni & Booth, Heather, 2022. "Thirty years on: A review of the Lee-Carter method for forecasting mortality," SocArXiv 8u34d, Center for Open Science.
    6. Colin O’hare & Youwei Li, 2017. "Modelling mortality: are we heading in the right direction?," Applied Economics, Taylor & Francis Journals, vol. 49(2), pages 170-187, January.
    7. 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.
    8. Jaap Spreeuw & Iqbal Owadally & Muhammad Kashif, 2022. "Projecting Mortality Rates Using a Markov Chain," Mathematics, MDPI, vol. 10(7), pages 1-18, April.
    9. Rachel WINGENBACH & Jong-Min KIM & Hojin JUNG, 2020. "Living Longer in High Longevity Risk," JODE - Journal of Demographic Economics, Cambridge University Press, vol. 86(1), pages 47-86, March.
    10. Man Chung Fung & Gareth W. Peters & Pavel V. Shevchenko, 2017. "Cohort effects in mortality modelling: a Bayesian state-space approach," Papers 1703.08282, arXiv.org.
    11. Boumezoued, Alexandre & Elfassihi, Amal, 2021. "Mortality data correction in the absence of monthly fertility records," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 486-508.
    12. Alexandre Boumezoued & Amal Elfassihi, 2020. "Mortality data correction in the absence of monthly fertility records," Working Papers hal-02634631, HAL.
    13. Bravo, Jorge M. & Ayuso, Mercedes & Holzmann, Robert & Palmer, Edward, 2021. "Addressing the life expectancy gap in pension policy," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 200-221.
    14. Man Chung Fung & Gareth W. Peters & Pavel V. Shevchenko, 2016. "A unified approach to mortality modelling using state-space framework: characterisation, identification, estimation and forecasting," Papers 1605.09484, arXiv.org.
    15. Hunt, Andrew & Blake, David, 2015. "Modelling longevity bonds: Analysing the Swiss Re Kortis bond," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 12-29.
    16. Han Lin Shang & Steven Haberman, 2020. "Retiree Mortality Forecasting: A Partial Age-Range or a Full Age-Range Model?," Risks, MDPI, vol. 8(3), pages 1-11, July.
    17. Katrien Antonio & Anastasios Bardoutsos & Wilbert Ouburg, 2015. "Bayesian Poisson log-bilinear models for mortality projections with multiple populations," Working Papers Department of Accountancy, Finance and Insurance (AFI), Leuven 485564, KU Leuven, Faculty of Economics and Business (FEB), Department of Accountancy, Finance and Insurance (AFI), Leuven.
    18. Susanna Levantesi & Virginia Pizzorusso, 2019. "Application of Machine Learning to Mortality Modeling and Forecasting," Risks, MDPI, vol. 7(1), pages 1-19, February.
    19. Colin O’hare & Youwei Li, 2017. "Models of mortality rates – analysing the residuals," Applied Economics, Taylor & Francis Journals, vol. 49(52), pages 5309-5323, November.
    20. Doukhan, P. & Pommeret, D. & Rynkiewicz, J. & Salhi, Y., 2017. "A class of random field memory models for mortality forecasting," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 97-110.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1550-:d:411425. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.