Beyond the highest life expectancy: construction of proxy upper and lower life expectancy bounds

  • Jia Liu
  • Jackie LiEmail author


The strong, persistent linear trend of the highest period life expectancy of females at birth, namely best-performance life expectancy, is an interesting global phenomenon which has already lasted for about 150 years. In this article, we study both the highest and lowest period life expectancies of a group of more developed countries and areas, and exploit their recent trends to construct approximate upper and lower bounds as a supplementary tool for future projections. We also seek two modifications of this proposed approach. First, despite that it has remained largely an empirical observation, we intend to examine the use of extreme value theory to provide a more theoretical framework for both the highest and lowest life expectancies. Second, we construct two hypothetical populations with each age experiencing the lowest or highest mortality rate amongst all the populations considered, and extrapolate their life expectancy trends into the future. The resulting life expectancy bounds perform reasonably well in our backtesting exercise and can potentially complement the usual application of a stochastic mortality model to the data of a single country.


Best-performance life expectancy Upper and lower bounds Extreme value theory Generalised extreme value distribution Maxima and minima Lee–Carter models 



The authors would like to thank the editor and the referees for their valuable comments and suggestions which greatly enhance the presentation of this paper. The authors also thank Bowen Yang for her research assistance in the initial stage of this project.


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Actuarial Studies and Business AnalyticsMacquarie UniversitySydneyAustralia

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