KEEPING ABREAST OF MORTALITY CHANGE
J H Pollard (Macquarie University, NSW 2109, Australia)
Actuaries have always taken account of mortality improvements when pricing life annuities. The usual approach is to produce a special generational life table for each cohort of lives from an initial cross sectional (period) life table, by making assumptions about mortality improvement since the date of the period table and assumptions about mortality change during the future lifetime of the annuitant. The methods developed in this paper allow the calculation of generational life annuities and life expectancies from the initial period table with only a few lines of arithmetic, obviating the need for sets of generational tables and revision of these tables when the rate of mortality change itself changes.
The methods are approximate and are based on the Gompertz “law” of mortality, so popular in years gone by. The answers they provide are very accurate and well within the range of error implied by the uncertainty in the assumed rate of future mortality improvement.