Actuaries need to project mortality rates into the far future for calculating present values of pension and annuity liabilities.  In an earlier post Stephen wrote about the advantages of stochastic projection methods.  One method we might try is the two-dimensional P-spline method with the simple assumption that the number of deaths at age i in year j follows a Poisson distribution (Brouhns, et al, 2002).  Figure 1 shows observed and fitted log mortalities for the cross-section of the mortality surface for age 70 with this method.

Figure 1.  Observed log(mortality) rates with fitted P-spline for underlying average.  ONS data for males in England & Wales.

At first sight, all seems well - the fit seems perfectly…

In February 2009 a variation on the Lee-Carter model for smoothing and projecting mortality rates was presented to the Faculty of Actuaries.  A key question for any projection model is whether the process being modelled is stable.  If the process is not stable, then a model assuming it is stable will give misleading projections.  Equally, a model which makes projections by placing a greater emphasis on recent data will be better able to identify a change in tempo of the underlying process.

We take the mortality hazard rates for males in England and Wales and calculate the relative mortality improvement, i.e. the improvement at age x in year y is:

1 - μ_x,y / μ_x,y-1

where the rates μ_x,y have been locally…

Public-health officials typically allocate their resources using evidence-based methods. They know their annual budget for spending on health measures, and they typically want to save as many lives as they can with that fixed budget. A first step when looking at how to allocate resources would be to see the distribution of deaths by age, as shown below for males in the United Kingdom between 2004 and 2006:

From the above graph it would seem to make sense to allocate resources to diseases and ailments of old age, since this is where the vast bulk of deaths are in modern societies. However, public-health officials also know that saving the life of a new-born child is better than saving the life of a centenarian, if for…