SSAP62: 2002, Q82
I am also getting a few emails about this question – a few people are confused about the calculation of the liabilities prior to reinsurance (in particular the 0.75 and 0.25 terms).
The policy was written 10/1 and it is currently 12/31, and so 3 months (25%) of the policy have elapsed. Therefore 25% of the premium has been earned. Based on this 25%, we can establish the two components of the liability:
-Unearned premium reserve (UEPR) – 75% of the liability is unearned. Therefore UEPR = 75% * WP = 75% * 25
-Loss Reserves: note that the loss ratio of 60% is based on the earned premiums. EP = 25% * 25. Therefore reserves=0.6*(0.25*25).
A common mistake in this question is to set the liabilities as 60% of 25 (ie the entire liability is loss reserves). We can not do this though as the premium has not been earned entirely – the assumption is that the insurer will incur losses uniformly throughout the year.