# 3. Use of life tables for probability calculations

As well as being the most recent actuarially determined record of mortality rates, the 2010-12 Tables can be used to project the probabilities of persons living or dying at some time in the future. This does, however, require an assumption on what will happen to mortality rates over the intervening period.

The simplest assumption is that mortality rates remain unchanged at the 2010-12 level. However, the continuing improvement in mortality exhibited in these Tables suggests that this assumption will tend to underestimate survival probabilities.

A range of assumptions can be made about future mortality improvements. Appendix E contains the two series of improvement factors derived from the historical trends in Australian mortality improvement over the last 25 years and 125 years. These factors can be applied to the mortality rates included in the current Life Tables to obtain projections of future mortality and life expectancy scenarios.

The process for incorporating future improvements can be expressed in the following mathematical form:

where

is the mortality rate at age

xin yeart;is the mortality rate reported for age

xin the current Tables; andis the rate of improvement at age

xas shown in Appendix E.

Other mortality functions can then be calculated using the formulae given in section 2.3.

An example of how to apply this formula is given below:

Consider a 35 year old female. Her mortality in 2011 is given in the current Life Tables as 0.000513. That is, = 0.000513

25 year improvement factors | 125 year improvement factors | |
---|---|---|

0.000513 | 0.000513 | |

The table below sets out the calculation of the projected mortality rate for a 35 year old female in future years —for *t *=2012, 2015 and 2050 — using the two improvement scenarios.

The two sets of improvement factors given in Appendix E should be treated as illustrative rather than forecasts. What the future will bring cannot be known. Using a particular set of factors allows the impact of a given scenario on mortality rates and associated life table functions to be quantified. It cannot say anything about what mortality rates will actually be. The differences in the projected rates under the two scenarios presented here highlight the uncertainty associated with modelling future mortality.

The importance of allowing for future improvements in mortality rates depends on the purpose of the calculations being carried out, the ages involved and the time span that is being considered. Clearly, the longer the time span being considered, the more significant will be the effect of mortality improvements. At the same time, the longer the time span being considered, the greater will be the uncertainty surrounding the projected rates. Similarly, the higher the improvement factors the more quickly the projected rates will diverge from the current rates.

**Appendices**