Exploring Life Insurance Underwriting Business: The Mathematical Effect of Plateaus and the Implications on Smoothed Mortality Estimation Involving Interpolation

Abstract

Parametric laws provide a structured theoretical framework of estimating and predicting mortality rates. In spite of its utility, it seems parsimonious models are rarely deployed to detect kinks. Furthermore, the practical application in assessing the impact of kinks on policy values for various life insurance products remains unexplored essentially concerning the sensitivity of these values to changes in mortality parameters. Mortality modelling is a crucial aspect of life insurance underwriting with applications in life annuity, pension plans and healthcare. Parsimonious mortality models often rely on parametric assumptions which can be restrictive and sensitive to model misspecification. Insurers must understand how adjustments in mortality assumptions and economic variables impact the valuation of life policies. These considerations are critical for designing sustainable insurance products and mitigating financial risks. To bridge these gaps, this paper explores the theoretical underpinnings of interpolation. The paper presents a non-parametric approach to mortality modelling using Everett’s interpolation. The method provides a flexible and data-driven framework for estimating mortality rates allowing for more accurate capture of age specific patterns. The objective is to detect wavy kinks and the impacts on mortality rate trajectories. In spite of the observed kinks, the results confirm that the interpolative approach provides improved and robust estimates of mortality rates when compared with the parsimonious laws where parameters are estimated with no guarantee of conforming to the globally acceptable intervals. Although perinatal mortality is inadmissible in the model, computational evidence revealed that mortality rate intensities significantly declined within ages 9 and 11.