Over-dispersion (reprise for actuaries)

(Jan 3, 2010)

In my previous post I illustrated the effects of over-dispersion in population data.  Of course, an actuary could quite properly ask: why use ONS data?  The CMI data set on assured lives might be felt to be a better guide to the mortality of pensioners, although Stephen has raised a question mark over this assumption in the past.

Figure 1 illustrates what happens with the CMI data set. The over-dispersion parameter is much smaller at 1.82, so the Poisson model gives a reasonable forecast.  Note that the over-dispersion in the CMI data comes from a different source, namely the presence of duplicates causing extra variability in death counts.  However, the same approach to over-dispersion works regardless of the…

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Tags: over-dispersion, duplicates, mortality projections, ICA, Solvency II

Over-dispersion

(Dec 9, 2009)

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.

Overdispersion

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

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Tags: over-dispersion, mortality projections, mortality improvements

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