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A Bayesian Comparison of Models for Changing Mortalities toward Evaluating Longevity Risk in Japan

Author

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  • Kogure Atsuyuki

    (Keio University, Japan)

  • Kitsukawa Kenji

    (Daiwa Securities SMBC, Japan)

  • Kurachi Yoshiyuki

    (University of Tokyo, Japan)

Abstract

We present a Bayesian approach to compare models for forecasting mortality rates under the framework of the Lee-Carter methodology. We consider the original normal log-bilinear formulation of the methodology as well as the recently proposed Poisson log-bilinear formulation. For each formulation, we compare three models: the deterministic trend model, the stochastic trend model and the stationary (no trend) model, each of which represents a different future scenario for changing mortalities. Markov-chain Monte Carlo methods are used to sample the predictive distributions from each model and to calculate the marginal likelihoods for the model selection. The approach is applied to Japanese male mortality rates from 1970 to 2003. The results show that the stochastic trend model is most appropriate for forecasting mortality rates both for the normal and the Poisson formulation. We then use the selected model to evaluate longevity risk in Japan by calculating the posterior predictive distributions of the life annuities for the population at age 65.

Suggested Citation

  • Kogure Atsuyuki & Kitsukawa Kenji & Kurachi Yoshiyuki, 2009. "A Bayesian Comparison of Models for Changing Mortalities toward Evaluating Longevity Risk in Japan," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 3(2), pages 1-22, April.
    • Handle: RePEc:bpj:apjrin:v:3:y:2009:i:2:n:1
    DOI: 10.2202/2153-3792.1036
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    References listed on IDEAS

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    1. 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.
    2. Olivieri, Annamaria, 2001. "Uncertainty in mortality projections: an actuarial perspective," Insurance: Mathematics and Economics, Elsevier, vol. 29(2), pages 231-245, October.
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    4. 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.
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    Citations

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    Cited by:

    1. Qian Lu & Katja Hanewald & Xiaojun Wang, 2021. "Subnational Mortality Modelling: A Bayesian Hierarchical Model with Common Factors," Risks, MDPI, vol. 9(11), pages 1-21, November.
    2. 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.
    3. Selin Ozen & c{S}ule c{S}ahin, 2021. "A Two-Population Mortality Model to Assess Longevity Basis Risk," Papers 2101.06690, arXiv.org.
    4. Li, Hong & De Waegenaere, Anja & Melenberg, Bertrand, 2015. "The choice of sample size for mortality forecasting: A Bayesian learning approach," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 153-168.
    5. 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.
    6. 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.
    7. Yang, Bowen & Li, Jackie & Balasooriya, Uditha, 2015. "Using bootstrapping to incorporate model error for risk-neutral pricing of longevity risk," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 16-27.
    8. 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.
    9. Jackie Li & Atsuyuki Kogure, 2021. "Bayesian Mixture Modelling for Mortality Projection," Risks, MDPI, vol. 9(4), pages 1-12, April.
    10. Jackie Li & Atsuyuki Kogure & Jia Liu, 2019. "Multivariate Risk-Neutral Pricing of Reverse Mortgages under the Bayesian Framework," Risks, MDPI, vol. 7(1), pages 1-12, January.
    11. Selin Özen & Şule Şahin, 2021. "A Two-Population Mortality Model to Assess Longevity Basis Risk," Risks, MDPI, vol. 9(2), pages 1-19, February.
    12. Kogure, Atsuyuki & Kurachi, Yoshiyuki, 2010. "A Bayesian approach to pricing longevity risk based on risk-neutral predictive distributions," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 162-172, February.
    13. 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.

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