Validation With Simulations
ACtuArIeS need deCreMent tAbleS to do most of their work.
those tables don’t exist unless other actuaries have created them. Since
we are always working with samples, how can we know if the tables
we create are sufficiently representative of the true but unknowable
underlying decrement table for the lives under study?
Actuaries in the past always have relied on having a large enough sample of
experience data that the rates for the table don’t differ much from the observed
rates. When we don’t have enough data,
we don’t have confidence that our graduation (or curve-fitting) will find us a
Changing the Technique
In “Mortality Rates at Oldest Ages,” a
paper that I presented at the Society
of Actuaries 2011 Living to 100 Symposium, I proposed a new technique to
address the problem. It has the advantage of being applicable to virtually any
type of table construction, regardless of
the method used, and it is simple enough
that most actuaries should be able to apply it successfully.
My idea involves constructing a table
incorporating the data available and a
reasonable method, using that table and
the starting population from the data to
randomly generate many sets of deaths
(or lapses, or whatever decrement is be-
ing studied), and finally applying the
for each. I will refer here to the results
for only one of the 12 tests, a Gompertz-
shaped base table and an improvement
scale that contains a cohort effect.
same construction method to each of
the simulated deaths. This allows us to
see from the means and standard deviations of the mortality rates how much
variation we should expect in the table.
We also are able to compare the relationship between the experience table and
the constructed table for both the original data and each simulated set of data.
These tests will indicate how reliable the
constructed table is likely to be, given
the experience we had to work with.
The example that I use here is the
same one you can find in my longer
paper. The experience is Canadian
population deaths for ages 95 and up,
for 1970 to 2005. I obtained the death
records from www.mortality.org. My
method involves inferring exposure
as well as determining mortality rates,
but the actual method is not relevant
to the example.
Since I was more concerned about determining the effectiveness of the method
than in finding a particular table, I tested
the method using three different base mortality tables and four improvement scales