Need advice on IBNR & case reserves adequacy testing

[Jason]

Was hoping you guys could share a few pointers with me on how to assess the risk of a property/casualty company's loss reserve (case reserves + IBNR) adequacy.

For instance, maybe if the company only uses a single method (such as Chain ladder on paid claims) without any others as a check, then that would make the estimate inhrently riskier than if there were a few methods employed and the differences explained?

Any thoughts on this?

[joeorez]

I'm sure my more mathematical colleagues will rip the following to shreds, but as a quick and dirty measure how about calculating the empirical coefficient of variation (standard deviation/mean) of each column's age-to-age factors?

The larger the CVs, the riskier are the reserves.

[JohnGalt]

Originally Posted by Jason

For instance, maybe if the company only uses a single method (such as Chain ladder on paid claims) without any others as a check, then that would make the estimate inhrently riskier than if there were a few methods employed and the differences explained?

Any thoughts on this?

Maybe this would be less risky, because the company wouldn't be able to pick the number it wants ahead of time and then choose the method that gets them clostest to that number!

Joe, I'm not sure about your approach. I think if you're doing a review in, say, March, that a property line will have a higher CV than GL, just because the 3 --> 15 factor will be huge then quickly converge to 1. Surely the reserve is less risky than GL though.

John

[Mobile Actuary]

I just received yesterday a "Forum" containing a 100 pp (or so) white paper on this topic. The short answer is, we don't know how to quantify variability in reserve estimates, but we're working on it, and have lots of good ideas.

Having said that, having several methods in your review should force you to examine the accuracy of the underlying assumptions in each in considering why the answers are different. That process should lead you to reserves that are more fully considered and better supported.

[Jason]

Thanks for the replies.

Mobile Actuary, to determine variability in loss reserve estimates, what about stochastic methods that calculate the standard deviation of the estimates? Would these be a good indicator of the variability?

[Abnormal]

Jason,

That will give you a measure of the variability of the estimates but without knowing what the actual ultimate losses are I'm not sure it tells you a lot.

If memory serves correctly one of Ben Zehnwirth's papers addresses this in some detail. I'm not sure if it was published by the CAS or the IAA.

[Jason]

Thanks, Abnormal. Got the paper from the CAS website. Going through it.