Modelling Australian Life Tables with Advanced Ages

Abstract

During the past two decades, the number of people in Australia aged 85 years and over increased by 117.1%, compared with a total population growth of 34.8% over the same period. There are now over 4800 centenarians in Australia, up from 3623 in 2013, and projections are for further substantial increases. Existing life tables do not take into account the oldest among the population in a credible manner. Methods describing adult lifetimes up to very advanced ages and corresponding lifetables closed at the upper end are required.

A new model designed for this purpose, called the Smooth Threshold Life Table (STLT) model, was developed by Huang, Maller & Ning (2020). In this model, traditional actuarial methods were augmented by extreme value technology, and the distribution so developed was shown to fit well to a large set of Netherlands data containing birth cohorts dating back to 1893.

The present paper reports results from fitting the STLT model to Australian mortality data compiled from the Human Mortality Database together with data from ABS. In almost all cases analyzed the STLT model fits the Australian data better than a variety of existing mortality models. The parameters in the STLT model, including the highest attained age within a cohort, which can be used to close a life table, are estimated objectively by maximum likelihood.

Keywords: Advanced Age Mortality, Extreme Value Theory, Generalized Pareto Distribution, Gompertz Model, Australian Data

JEL Classification: G22 - Insurance; Insurance Companies; Actuarial Studies