Wavy kinks kinematics and the impact on instantaneous mortality rate intensities

Abstract

This study proposes an innovative approach to mortality modelling using Stirling interpolation, a numerical analysis technique that enables the estimation of mortality rates at intermediate ages or time points. The results show that the interpolation approach provides more accurate and robust estimates of mortality rates particularly at intermediate ages points. This study demonstrates the potential of Stirling interpolation in mortality modelling and highlights its advantages over traditional methods. The approach has significant implications for actuarial science including life insurance, annuities and pension funds. Mortality modelling is a crucial aspect of actuarial science as it enables the estimation of future mortality rates and the calculation of life insurance reserves, annuity values and pension fund liabilities. Traditional mortality models, such as the parametric model have been widely used in the insurance practice. Stirling interpolation is deployed as an alternative approach to mortality modelling. The objective of the study is to detect kinks and identify the impact on the force of mortality using Stirling’s interpolation. From the results obtained, the interpolated value for the year shows a comparative significant increase between ages 9 and above or decrease from age 5 and 8, this could indicate trends in the population's health such as an improvement or worsening in health conditions, access to healthcare or public health interventions. Though the methodology has the potential to detect kinks due to random shocks in mortality rates, computational evidence confirm that the interpolative approach provides improved, robust and reasonably lower mortality estimates.