Feldblum WC 2002 #27

[Rice]

Policy Year 2000 EP as of 12/31/01 = $90 million
Policy audits occur 6 months after expiration and produce a 10% increase in premium
Policy term is 12 months

a) What is the PY 2000 EP after all appropriate adjustments to premium development (and other stuff)?

The factor the CAS solution uses for premium development is 1.1/1.05. The 1.05 is the 12 to 24 month development factor. But why not just use 1.05 instead of 1.1/1.05 (which is 1.0476), since were talking premium development and premium is developing by 1.05?

The same situation occurs in part b) dealing with the benefit change.

What's more, b) asks: What are the PY 2000 losses, yet the answer includes the provision for LAE. Wouldn't they have specifically asked for loss and LAE if they wanted both included, like they did for part c)?

[oopsieny]

Suppose X is the written premium of PY 2000
at 12/31/01, only 1/2 of the premium had been audited and effected by the factor of 1.1 (10% increase post audit). So the formula is
1.1*.5*X +.5X = 90 million. Solve for X to get the WP for PY 2000, which X equals 85.714 million.
Then, the fully earned premium for PY 2000 would be 1.1*85.714 = 92.286
The Premium development factor is then 92.286/90 = 1.0476

[lmmrrsn]

Hey Rice:

a) I agree with you. The answer doesn't seem to take the mid-year rate increase into account.

b) I think that's a mistake in the answer.

I have asked Sholom Feldblum to comment on a) and I'll let you know what he thinks when I hear from him.

[Examinator]

Can it be understood as follows?

Premium develops 10% updaward. After one year, you know it's developed 5% upward. The remaining development is 4.8% upward, or 1.100/1.050 - 1.000.