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Incorporating hierarchical credibility theory into modelling of multi-country mortality rates

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  • Tsai, Cary Chi-Liang
  • Wu, Adelaide Di

Abstract

A hierarchical credibility model is a generalization of the Bühlmann credibility model and the Bühlmann–Straub credibility model with a tree structure of four or more levels. This paper aims to incorporate hierarchical credibility theory, which is used in property and casualty insurance, to model multi-country mortality rates. The forecasting performances of the three/four/five-level hierarchical credibility models are compared with those of the classical Lee–Carter model and its three extensions for multiple populations (the joint- k, the co-integrated, and the augmented common factor Lee–Carter models). Numerical illustrations based on mortality data from the Human Mortality Database for both genders of the US, the UK and Japan with a series of fitting year spans and three forecasting periods show that the hierarchical credibility approach contributes to more accurate forecasts measured by the AMAPE (average of mean absolute percentage errors). Finally, a stochastic version of the proposed hierarchical credibility mortality model is also proposed, which can be used to construct predictive intervals on the projected mortality rates and to conduct stochastic simulations for applications.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:91:y:2020:i:c:p:37-54
    DOI: 10.1016/j.insmatheco.2020.01.001
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    References listed on IDEAS

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    Cited by:

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    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. Salazar García, Juan Fernando & Guzmán Aguilar, Diana Sirley & Hoyos Nieto, Daniel Arturo, 2023. "Modelación de una prima de seguros mediante la aplicación de métodos actuariales, teoría de fallas y Black-Scholes en la salud en Colombia [Modelling of an insurance premium through the application," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 35(1), pages 330-359, June.

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