This blog brings together two pieces of work. The first is the paper we presented to the Institute and Faculty of Actuaries, "A stochastic implementation of the APCI model for mortality projections", which will appear in the British Actuarial Journal. The second is a previous blog where I examined the role of constraints in models of mortality.

The survivor function from age \(x\) to age \(x+t\), denoted \({}_tp_x\) by actuaries, is a useful tool in mortality work. As mentioned in one of our earliest blogs, a basic feature is that the expected time lived is the area under the survival curve, i.e. the integral of \({}_tp_x\). This is easy to express in visual terms, but it often requires numerical integration if there is no closed-form expression for the integral of the survival curve.

This blog has two aims: first, to describe how we go about simulation in the Projections Toolkit; second, to emphasize the important role a model has in determining the width of the confidence interval of the forecast.

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