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A Bühlmann Credibility Approach to Modeling Mortality Rates

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  • Cary Chi-Liang Tsai
  • Tzuling Lin

Abstract

In this article, we first propose a Bühlmann nonparametric credibility approach to forecasting mortality rates, and we then compare forecasting performances between the proposed Bühlmann approach and the Lee-Carter/Cairns-Blake-Dowd (CBD) models. Empirical results based on mortality data for both genders of Japan, the United Kingdom, and the United States with two age spans, a wide range of fitting year spans, and three forecasting periods show that the credibility approach contributes to much better forecasting performances measured by the mean absolute percentage error. Moreover, we give an informative credibility interpretation regarding the average decrements of an individual time trend for age x and a group time trend for all ages, and we discuss the effects of the slope and intercept of the linear functions for the forecasted mortality rates under the proposed Bühlmann nonparametric credibility approach and the Lee-Carter/CBD models. Finally, we also estimate the parameters of the Bühlmann credibility approach in a semiparametric framework, and we provide a stochastic version of forecasting mortality rates for the Bühlmann credibility approach.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:uaajxx:v:21:y:2017:i:2:p:204-227
    DOI: 10.1080/10920277.2016.1246253
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    Cited by:

    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. 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.
    3. Norkhairunnisa Redzwan & Rozita Ramli, 2022. "A Bibliometric Analysis of Research on Stochastic Mortality Modelling and Forecasting," Risks, MDPI, vol. 10(10), pages 1-17, October.
    4. Tsai, Cary Chi-Liang & Kim, Seyeon, 2022. "Model mortality rates using property and casualty insurance reserving methods," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 326-340.
    5. 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.

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