Bayesian joint modelling of life expectancy and healthy life expectancy and valuation of retirement village contract

Life expectancy and healthy life expectancy are both important indicators of population wellbeing, reflecting the expected length of life and duraiton of healthy living respectively. While extensive research has focused on projecting life expectancy, very few have investigated the projection and simulation of healthy life expectancy and examined its potential applications. In this paper, we establish a Bayesian approach to jointly model life expectancy and healthy life expectancy. We apply this approach to the population data of various countries, demonstrating its ability to provide accurate forecasts, generate probability intervals to capture future uncertainty, and estimate missing data values. We then illustrate an application of the Bayesian model in valuing a retirement village contract. Many Australian seniors choose retirement villages for the community support they offer, transitioning to aged care facilities as their health declines. The value of the accommodation service depends on the resident's length of stay, which can be approximated by healthy life expectancy. The proposed Bayesian model can produce a sampled distribution of the contract's net present value, providing a useful risk management tool for retirement village operators. Our findings emphasise the importance of considering healthy life expectancy in policies on public health and retirement.