Between the lines

(May 26, 2011)

Actuaries make great use of so-called standard tables.  These are annual probabilities at each whole age for males and females.  However, often mortality rates are required at ages which are not whole numbers.  Since the rates in standard tables change relatively smoothly from one age to the next, a natural approach is to use interpolation to approximate the rates between whole ages.

The simplest approach is linear interpolation, which uses the rates at ages on either side of the target age.  However, this suffers from the drawback that mortality rates at post-retirement ages increase exponentially with age.  The consequence of this is that linearly interpolated rates are always too high and will thus slightly…

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Tags: interpolation, approximation

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