The Gompertz - Makeham Coupling as a Dynamic Life Table

Abstract

A very famous law of mortality was introduced by Gompertz in 1825 in [G] . In 1860 Makeham introduced in [M] a modification to obtain another law of mortality. Both these laws assume that the population under consideration is stable. The two laws differ by a constant term in the force of mortality. The updated approach to the study of population presume that mortality changes over time. The difference stems from observing that the expectancy of life changes over the years. There were made various attempts to introduce dynamic life tables, and the Lee-Carter model has this advantage. The Lee-Carter model in [LC] describes better the mortality under changes over time as was shown recently by ([M ) . We intend to study the difference arising from a fixed change in the force of mortality and the Gompertz and Makeham cases may serve to demonstrate such a change. The difference in the expectancy of life in both cases affects directly the corresponding life tables, and consequently the annuities (for life, term annuitie and deferred ), as well as the assurances (whole life, term and endowment) , and the premiums and reserves in the various cases. The changes in a stable life table model may serve to evaluate the changes that arise in terms of a sensitive analysis of various assurance plans. Consequently there results a tool to cope with evaluating the effect of change in the force of mortality.