Who Wants to Live Forever? Exploring the Frontiers of Human Life Span Using Extreme Value Theory

Jorge M. Bravo , Universidade Nova de Lisboa (NOVA IMS)
Edviges Coelho, Statistics Portugal

In this paper we use Extreme Value Theory (EVT) to model human mortality at extremely high ages using a unique dataset of the exact ages at death (in days), sex and birth cohort of all Portuguese residents who died between 1980 and 2018 at high age. Contrary to previous studies that used annual aggregated mortality data, we work with reliable mortality data from official deaths registration provided by Statistics Portugal. To determine the threshold age in the peaks-over-threshold (POT) method, we conduct both a period and cohort analysis and empirically investigate alternative methods, including the threshold life table method, the Pickands (1975) method, the empirical mean excess function plot method, Monte Carlo simulation methods, automatic selection procedures and an Extreme Value Mixture Model. We then use the model to statistically estimate the life table highest attained age over a period of almost forty consecutive years and analyse gender differences observed in the data. This will allow us not only to analyse the dynamics of extreme longevity risk by age and gender, but also over time. Additionally, model the dynamics of the limiting age over time and derive point forecasts and prediction intervals for the highest attained age. This is crucial in forecasting the age structure of population over time. We the used the model result to the estimate the ultimate age, the maximum age at death and the price of life annuity contracts and corresponding risk measures (VaR, Expected Shortfall).

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 Presented in Session P2. Poster Session Ageing, Health and Mortality