Cumulative claim development factors (a.k.a. age-to-ultimate factors and claim development factors to ultimate) are calculated by successive multiplications beginning with the tail factor and the oldest age-to-age factor and projects the total growth over the remaining valuations.
Cumulative CDFs are often greatest for the most recent AYs and the smallest for the oldest accident years.
Actuaries refer to the most recent, less-developed AYs as immature and the oldest, most-developed AYs as mature.
Calculating CDFs
Using the selected age-to-age factors from earlier exercises, calculate the following:
- Selected tail/ultimate factor = 1.00
- CDF at 4 years= (selected tail factor) x (selected development factor 4-5 years) = 1.00 x 1.125= 1.125
- CDF at 3 years= (selected tail factor) x (selected development factor 4-5 years) x (selected development factor 3-4 years)
= (CDF at 4 years) x (selected development factor 3-4 years) = 1.127 x 1.125 = 1.267 - Continue in this manner until computing the Reported CDF at 1 year
- = (CDF at 2 years) x (selected development factor 1-2 years) = 2.437
Try some of the calculation in the below exercise and see that if you have got it right!