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A Linear Regression Approach to Modeling Mortality Rates of Different Forms

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  • Cary Chi-Liang Tsai
  • Shuai Yang

Abstract

In this article, we propose a linear regression approach to modeling mortality rates of different forms. First, we repeat to fit a mortality sequence for each of K years (called the fitting years) with another mortality sequence of equal length for some year (called the base year) differing by tj years (j = 1, …, K) using a simple linear regression. Then we fit the sequences of the estimated slope and intercept parameters of length K, respectively, with the sequence of {tj} by each of the simple linear regression and random walk with drift models. The sequences of the fitted slope and intercept parameters can be used for forecasting deterministic and stochastic mortality rates. Forecasting performances are compared among these two approaches and the Lee-Carter model. The CBD model is also included for comparisons for an elderly age group. Moreover, we give a central-death-rate–linked security to hedge mortality/longevity risks. Optimal units, purchased from the special purpose vehicle, which maximize the hedge effectiveness for life insurers and annuity providers, respectively, are derived and can be expressed in terms of the cumulative distribution function of the standard normal random variable. A measure with hedge cost involved, called hedge effectiveness rate, for comparing risk reduction amount per dollar spent among mortality models is proposed. Finally, numerical examples are presented for illustrations.

Suggested Citation

  • Cary Chi-Liang Tsai & Shuai Yang, 2015. "A Linear Regression Approach to Modeling Mortality Rates of Different Forms," North American Actuarial Journal, Taylor & Francis Journals, vol. 19(1), pages 1-23, January.
  • Handle: RePEc:taf:uaajxx:v:19:y:2015:i:1:p:1-23
    DOI: 10.1080/10920277.2014.975252
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    Citations

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    Cited by:

    1. Osman Gulseven, 2016. "Forecasting Population and Demographic Composition of Kuwait Until 2030," International Journal of Economics and Financial Issues, Econjournals, vol. 6(4), pages 1429-1435.
    2. Tsai, Cary Chi-Liang & Cheng, Echo Sihan, 2021. "Incorporating statistical clustering methods into mortality models to improve forecasting performances," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 42-62.
    3. 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.
    4. Cadena, Meitner & Denuit, Michel, 2016. "Semi-parametric accelerated hazard relational models with applications to mortality projections," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 1-16.
    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.
    6. Francesca Di Iorio & Stefano Fachin, 2020. "Forecasting mortality rates and life expectancy in the year of Covid-19," DSS Empirical Economics and Econometrics Working Papers Series 2020/1, Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome.
    7. Apostolos Bozikas & Georgios Pitselis, 2019. "Credible Regression Approaches to Forecast Mortality for Populations with Limited Data," Risks, MDPI, vol. 7(1), pages 1-22, February.
    8. Tzuling Lin & Cary Chi‐Liang Tsai, 2023. "A new option for mortality–interest rates," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(2), pages 273-293, February.

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