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Bayesian Poisson log-bilinear models for mortality projections with multiple populations

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  • Katrien Antonio
  • Anastasios Bardoutsos
  • Wilbert Ouburg

Abstract

Life insurers, pension funds, health care providers and social security institutions face increasing expenses due to continuing improvements of mortality rates. The actuarial and demographic literature has introduced a myriad of (deterministic and stochastic) models to forecast mortality rates of single populations. This paper presents a Bayesian analysis of two related multi-population mortality models of log-bilinear type, designed for two or more populations. Using a larger set of data, multi-population mortality models allow joint modelling and projection of mortality rates by identifying characteristics shared by all subpopulations as well as sub-population specific effects on mortality. This is important when modeling and forecasting mortality of males and females, regions within a country and when dealing with index-based longevity hedges. Our first model is inspired by the two factor Lee & Carter model of Renshaw and Haberman (2003) and the common factor model of Carter and Lee (1992). The second model is the augmented common factor model of Li and Lee(2005). This paper approaches both models in a statistical way, using a Poisson distribution for the number of deaths at a certain age and in a certain time period. Moreover, we use Bayesian statistics to calibrate the models and to produce mortality forecasts. We develop the technicalities necessary for Markov Chain Monte Carlo ([MCMC]) simulations and provide software implementation (in R) for the models discussed in the paper. Key benefits of this approach are multiple. We jointly calibrate the Poisson likelihood for the number of deaths and the times series models imposed on the time dependent parameters, we enable full allowance for parameter uncertainty and we are able to handle missing data as well as small sample populations. We compare and contrast results from both models to the results obtained with a frequentist single population approach and a least squares estimation of the augmented common factor model.

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  • 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.
    • Handle: RePEc:ete:afiper:485564
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    References listed on IDEAS

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    3. Hong Li & Yang Lu, 2018. "A Bayesian non-parametric model for small population mortality," Post-Print hal-02419000, HAL.
    4. Jevtić, Petar & Regis, Luca, 2019. "A continuous-time stochastic model for the mortality surface of multiple populations," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 181-195.
    5. Wang, Ling & Chiu, Mei Choi & Wong, Hoi Ying, 2021. "Volterra mortality model: Actuarial valuation and risk management with long-range dependence," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 1-14.
    6. 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.
    7. Yaser Awad & Shaul K. Bar-Lev & Udi Makov, 2022. "A New Class of Counting Distributions Embedded in the Lee–Carter Model for Mortality Projections: A Bayesian Approach," Risks, MDPI, vol. 10(6), pages 1-17, May.
    8. Kira Henshaw & Waleed Hana & Corina Constantinescu & Dalia Khalil, 2023. "Dependence Modelling of Lifetimes in Egyptian Families," Risks, MDPI, vol. 11(1), pages 1-25, January.
    9. Wang, Pengjie & Pantelous, Athanasios A. & Vahid, Farshid, 2023. "Multi-population mortality projection: The augmented common factor model with structural breaks," International Journal of Forecasting, Elsevier, vol. 39(1), pages 450-469.
    10. Patrizio Vanella & Ugofilippo Basellini & Berit Lange, 2020. "Assessing Excess Mortality in Times of Pandemics Based on Principal Component Analysis of Weekly Mortality Data -- The Case of COVID-19," Working Papers axbhmxrs-o0viyh9z07m, French Institute for Demographic Studies.
    11. Ling Wang & Mei Choi Chiu & Hoi Ying Wong, 2020. "Volterra mortality model: Actuarial valuation and risk management with long-range dependence," Papers 2009.09572, arXiv.org.

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