Generating Mortality Rate Intensity for Life Insurance Applications through Novel Method of Successive Differencing Under the Parsimonious Generalised Makeham’s Framework

Abstract

Developing and implementing age dependent mortality rates in functional forms have presented critical modelling problems for life insurance and annuity firms thereby creating serious research gaps. A recurring problem with the existing life tables is that their underlying generating functions are not capable of showing any evidence that mortality at 10 declines. This observed irregularity in the age pattern of mortality is the prime motivation in the search for analytical functions which fully capture the observed variations of mortality with age. To fill the gaps identified, the study aims to develop specific life table function under the Generalised Makeham’s framework. The objectives of this study are to (i) compute the mortality rate intensities  (ii) compute the curve of deaths densities   (iii) compute the probability of deaths and then compare the common domain of definition of these measures. From the method of successive differencing employed to model, the male ageing parameter value fall within the globally accepted interval  for the. This method is superior to the method of maximum likelihood estimation which mostly violates the permissible interval of validity. Computational evidence from our analysis proves that under the Generalised Makeham’s law, the mortality rate intensity declines at .