IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v91y2020icp68-84.html
   My bibliography  Save this article

A hierarchical model for the joint mortality analysis of pension scheme data with missing covariates

Author

Listed:
  • Ungolo, Francesco
  • Kleinow, Torsten
  • Macdonald, Angus S.

Abstract

A hierarchical model is developed for the joint mortality analysis of pension scheme datasets. The proposed model allows for a rigorous statistical treatment of missing data. While our approach works for any missing data pattern, we are particularly interested in a scenario where some covariates are observed for members of one pension scheme but not the other. Therefore, our approach allows for the joint modelling of datasets which contain different information about individual lives. The proposed model generalizes the specification of parametric models when accounting for covariates. We consider parameter uncertainty using Bayesian techniques. Model parametrization is analysed in order to obtain an efficient MCMC sampler, and address model selection. The inferential framework described here accommodates any missing-data pattern, and turns out to be useful to analyse statistical relationships among covariates. Finally, we assess the financial impact of using the covariates, and of the optimal use of the whole available sample when combining data from different mortality experiences.

Suggested Citation

  • Ungolo, Francesco & Kleinow, Torsten & Macdonald, Angus S., 2020. "A hierarchical model for the joint mortality analysis of pension scheme data with missing covariates," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 68-84.
    • Handle: RePEc:eee:insuma:v:91:y:2020:i:c:p:68-84
    DOI: 10.1016/j.insmatheco.2020.01.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668720300032
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2020.01.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Richards, S. J. & Currie, I. D. & Ritchie, G. P., 2014. "A Value-at-Risk framework for longevity trend risk," British Actuarial Journal, Cambridge University Press, vol. 19(1), pages 116-139, March.
    2. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
    3. repec:dau:papers:123456789/6069 is not listed on IDEAS
    4. Richards, S. J., 2008. "Applying Survival Models to Pensioner Mortality Data," British Actuarial Journal, Cambridge University Press, vol. 14(2), pages 257-303, July.
    5. Macdonald, A.S., 1996. "An Actuarial Survey of Statistical Models for Decrement and Transition Data - I: Multiple State, Poisson and Binomial Models," British Actuarial Journal, Cambridge University Press, vol. 2(1), pages 129-155, April.
    6. Dickson,David C. M. & Hardy,Mary R. & Waters,Howard R., 2013. "Actuarial Mathematics for Life Contingent Risks," Cambridge Books, Cambridge University Press, number 9781107044074, October.
    7. 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.
    8. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    9. Macdonald, A.S., 1996. "An Actuarial Survey of Statistical Models for Decrement and Transition Data, III. Counting Process Models," British Actuarial Journal, Cambridge University Press, vol. 2(3), pages 703-726, August.
    10. Czado, Claudia & Delwarde, Antoine & Denuit, Michel, 2005. "Bayesian Poisson log-bilinear mortality projections," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 260-284, June.
    11. Richards, S. J., 2016. "Mis-estimation risk: measurement and impact," British Actuarial Journal, Cambridge University Press, vol. 21(3), pages 429-457, September.
    Full references (including those not matched with items on IDEAS)

    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. Barigou, Karim & Goffard, Pierre-Olivier & Loisel, Stéphane & Salhi, Yahia, 2023. "Bayesian model averaging for mortality forecasting using leave-future-out validation," International Journal of Forecasting, Elsevier, vol. 39(2), pages 674-690.
    2. Park, Byung-Jung & Zhang, Yunlong & Lord, Dominique, 2010. "Bayesian mixture modeling approach to account for heterogeneity in speed data," Transportation Research Part B: Methodological, Elsevier, vol. 44(5), pages 662-673, June.
    3. 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.
    4. Selin Özen & Şule Şahin, 2021. "A Two-Population Mortality Model to Assess Longevity Basis Risk," Risks, MDPI, vol. 9(2), pages 1-19, February.
    5. Kozumi, Hideo, 2004. "Posterior analysis of latent competing risk models by parallel tempering," Computational Statistics & Data Analysis, Elsevier, vol. 46(3), pages 441-458, June.
    6. Yuan Fang & Dimitris Karlis & Sanjeena Subedi, 2022. "Infinite Mixtures of Multivariate Normal-Inverse Gaussian Distributions for Clustering of Skewed Data," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 510-552, November.
    7. 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.
    8. Jackie Li & Atsuyuki Kogure, 2021. "Bayesian Mixture Modelling for Mortality Projection," Risks, MDPI, vol. 9(4), pages 1-12, April.
    9. M. Moghadam, 2013. "Extended risk classification in insurance industry," Quality & Quantity: International Journal of Methodology, Springer, vol. 47(3), pages 1385-1396, April.
    10. Jackie Li, 2014. "An application of MCMC simulation in mortality projection for populations with limited data," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 30(1), pages 1-48.
    11. Jia-Chiun Pan & Chih-Min Liu & Hai-Gwo Hwu & Guan-Hua Huang, 2015. "Allocation Variable-Based Probabilistic Algorithm to Deal with Label Switching Problem in Bayesian Mixture Models," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-23, October.
    12. Liu, Yanxin & Li, Johnny Siu-Hang, 2016. "It’s all in the hidden states: A longevity hedging strategy with an explicit measure of population basis risk," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 301-319.
    13. Weber, Anett & Steiner, Winfried J., 2021. "Modeling price response from retail sales: An empirical comparison of models with different representations of heterogeneity," European Journal of Operational Research, Elsevier, vol. 294(3), pages 843-859.
    14. Jaap Spreeuw & Iqbal Owadally & Muhammad Kashif, 2022. "Projecting Mortality Rates Using a Markov Chain," Mathematics, MDPI, vol. 10(7), pages 1-18, April.
    15. James Risk & Michael Ludkovski, 2015. "Statistical Emulators for Pricing and Hedging Longevity Risk Products," Papers 1508.00310, arXiv.org, revised Sep 2015.
    16. 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.
    17. Leung, Melvern & Fung, Man Chung & O’Hare, Colin, 2018. "A comparative study of pricing approaches for longevity instruments," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 95-116.
    18. Hong Li & Yang Lu, 2018. "A Bayesian non-parametric model for small population mortality," Post-Print hal-02419000, HAL.
    19. Jonathan Jaeger & Philippe Lambert, 2014. "Bayesian penalized smoothing approaches in models specified using differential equations with unknown error distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(12), pages 2709-2726, December.
    20. Panagiotis Papastamoulis & George Iliopoulos, 2013. "On the Convergence Rate of Random Permutation Sampler and ECR Algorithm in Missing Data Models," Methodology and Computing in Applied Probability, Springer, vol. 15(2), pages 293-304, June.

    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:eee:insuma:v:91:y:2020:i:c:p:68-84. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    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.