PDR Question

[GefilteFish144]

A co-worker of mine has a question regarding the premium deficiency reserve calculation. Despite having taken this exam 4 times, I've already forgotten how to answer it. Hope you can help.

Suppose an insurer writes a block of policies with written premium of $100m on July 1, 20x4. Acquisition costs are $20m and expected losses are 80m If by December 31, 20x4, incurred losses are 65m, and the insurer expects another 45m of incurred losses in the next 6 months, the DPAC is zero, and a premium deficiency reserve of $15m is set up on both GAAP and statutory statement". How do we get the 15m premium deficiency reserve ?

[Colymbosathon ecplecticos]

Assuming that the premium is to be earned linearly over the term, it appears that there is no PDR in your example.

The UPR is 50 and future expenses are 45. (I'm assuming that 45 is the PV of the future incurred loss, but since it's less than 50 it doesn't matter.)

[Avi]

If the DPAC is 0, doesn't that imply all the premium is already earned? I thought under GAAP, the DPAC and UEPR are earned at the same rate. If so, I still don't understand why there is a PDR of 15.

There is 100M WP which is now 100M EP.

20M Acquistion costs

Loss reserve of 65M.

There is 15M surplus left, but 45M of Expected, BUT UNINCURRED, losses.

Shouldn't the PDR be 30M?

[Colymbosathon ecplecticos]

I guess I should have added that I assumed a 12 month term for the policies.

at 12/31/xx

WP = 100 (not relevant)
EP = 50
UPR = 50
incurred losses to date = 65 (not relevant)
expected future incurred losses = 45

future incurred losses < UPR ==> no PDR (assuming no other expenses)

They had a really bad last six months of the year, but that doesn't let them earn the premium faster.

[GefilteFish144]

I think it might help to include the reference -- Feldblum Statutory Surplus paper, p. 8-9:

http://www.casact.org/library/studynotes/FeldblumSurplus.pdf

[Avi]

According to Feldblum, the DPAC is 10, not 0, matching the linear earning of the UEPR.


As such, The 65M Case and Bulk LR has no bearing.

There is 40M in UEPR and 10M in DPAC, for 50M total. There is an expected 65M in UNincurred losses. 65-40-10 = 15.

[GefilteFish144]

The paper actually says that inc. losses are $65M and the insurer expects "another $45M" in the next 6 months. That leads me to believe that he mean to say "another $65M", in which the numbers would make sense. It's just so difficult to imagine a Feldblum paper with a typo in it....

[Avi]

I think the 45 and 65 got reversed here as well.