Stochastic differential equations death rates models: the Portuguese case

In recent years, the increasing life expectancy of the world’s population, due to increased availability of prescribed medication, quality of health care services, quantity of health care institutions and quality of life, combined with a sharp decrease in birth rates over time, has proven to be a challenging problem for governments worldwide (particularly in developed countries). Both of these factors put at risk the sustainability of state-funded welfare programs (e.g., social security) and also lead to a decrease in available workforce and tax revenue (including social benefit contributions) in the near future. With the tendency for these problems to worsen in the next decades (severity varies between countries), it is of paramount importance to estimate the extension of human life in order to analyse the severity of this phenomenon. Stochastic differential equations have been used recently to model the evolution of death rates. In fact, such models have some advantages when compared to the deterministic ones since we can input random environmental fluctuations and evaluate the uncertainty in forecasts. The main goal of this paper is to apply and compare stochastic differential equations death rate models separately for each age and sex and forecast Portuguese death rates until the year 2030.