age-to-age paid loss development and age-to-ult factors

Question

I am studying ultimate claims. There it shows how to calculate the age-to-age paid loss-development factors by looking at the previous year claims amounts and their cumulative of claims to date. Then they magically use age-to-ult factor and multiply it by cumulative paid to-date to get the value of Estimated ultimate claims. How do I calculate the age-to-ult factor?

Answer 1

The age-to-ultimate factor is the product of the various age-to-age factors from the given age on. Typically, development stops after a certain age so all of the age-to-age factors are $1.0$ from some point on (there may be a tail factor as well).

So you can find the ultimate value by multiplying the latest paid loss by all of the age-to-age factors from that loss's age onwards.

For example, if the age-to-age factors are

• 12-24: $1.5$
• 24-36: $1.2$
• 36-48: $1.1$
• no more development past 48 months

then the 12-ultimate factor is $(1.5)(1.2)(1.1)=1.98$, and you would multiply the latest paid amount (presumably now aged 12 months) by this to get the ultimate projection.

Intuitively, the 12-24 factor takes the loss from 12 months (now) to 24 months; then the 24-36 factor takes it from 24 months to 36 months; the 36-48 factor takes it from 36 months to 48 months; at that point development stops, so it is at ultimate.