Hi B_actuary,
We only require an URR if the UPR (net of DAC) is expected to be inadequate to cover claims from unearned business. We know that product X has a loss ratio (including claims handling expenses) of 75% x 1.10 = 82.5%, and we also know that acquisition costs will be at most 15%. Hence, since net UPR (1-15%) > claims (82.5%) it's pretty clear that an unexpired risk reserve won't be needed.
A more detailed explanation follows:
In fact, we'd also allow for other factors such as investment income, rate changes, claims inflation, changes in terms and conditions etc when establishing whether an AURR is needed.
So, a more detailed process would be:
Calculate UPR for product X at the end of year 1 = 178.5
Multiply by LR (including claims handling expenses) (ie multiply by 82.5%)
Adjust the loss ratio to allow for rate changes, claims inflation etc (eg by dividing by (1+rate increase), not applicable in this question) to estimate the future claims on unearned business
Allow for investment income (assuming the average claim on unexpired risk occurs in 3 months' time, and no delays for notification / settlement say, ie multiply by 1.06^(-3/12))
Gives 178.5 x 82.5% x 1.06^(-3/12) = 145.13.
Now compare this to UPR net of DAC. Even if DAC does not decrease (so assuming DAC = 15% x UPR = 26.78), UPR net of DAC = 178.5-26.775 = 151.73. So the claims from unexpired risk are lower than UPR net of DAC. Hence, no AURR is required.
Last edited: Sep 18, 2011
