The Health Economics of Life Expectancy

Counting the Days before the Individual’s Roll Call

Résumé

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 e_x(male)< e_x(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.