Mortality Projection on Indonesia's Abridged Life Table to Determine the EPV of Term Annuity

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 .

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The Health Economics of Life Expectancy

Ogungbenle,

Ogwu,

Ogungbenle

2024

LJSIR

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For a life office, the potential deviations from the mortality assumptions applied in premium setting at the time of incepting contracts represents serious threats to its financial performance when underwriting life insurance policies including annuities. Furthermore, in view of the uncertainties associated with the complete expectation of life evolving from the inadequately modelled life expectancy as a form of mortality risk indicator, this study explores the CMI’s generalized Makeham’s mortality law which would be advantageous to compute complete life expectancies. When continuous parsimonious parametric mortality intensities are Makehamized, then the limiting value of the continuous whole life annuity function is construed to mean the complete life expectancy which is expressed in line with special functions such as incomplete upper gamma function for a homogeneous insured population. In this study, the objective are to (i) construct actuarial estimation of individual’s time remaining through single life parameterization from GM(1,2) (ii) construct closed form expressions for complete life expectancy using the properties of the special functions as applicable in classical mortality dynamics. To circumvent the need for any rigorous numerical procedures, the advanced technique of the Gradshteyn and Ryzhik’s analytic integral is applied in computing the complete life expectancies. From our results, it is apparent that ex(male)< ex(female). Specifically, within the interval 111<x<119 for women, there is a sharp decrease in complete life expectancies whereas for men within the interval 75<x<119, life expectancies sharply decrease confirming earlier exposure of men to mortality risk.

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Mortality Projection on Indonesia's Abridged Life Table to Determine the EPV of Term Annuity

Cited by 3 publications

References 10 publications

A mathematical modelling in determining the portion of Tabarru’ fund for sharia life insurance based on wakalah scheme

A mathematical modelling in determining the portion of Tabarru’ fund for sharia life insurance based on wakalah scheme

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

The Health Economics of Life Expectancy

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