2001 #30

[Examinator]

This question is from Brosius. It's also on page 57 of the (2004) All 10. I understand the question and the solution, but I'm having some trouble with the rust on my statistics.

The stimated standard deviation of the ratio of reported loss to ultimate loss at 12 months of development is 0.20 af the elimination of the cap.

Can someone refresh me on how, for EPV,
E[VAR(X|Y)] = E[(0.20^2)(Y^2)]?

[Examinator]

Nevermind. I'm not bright.

[Tommy Vercetti]

Hmm..
I am having problems with this too.
Can you tell me why?

[KidCA]

I think I know where they're getting it. It may be helpful to refer to earlier pages in All 10, with the "different application" of Bayesian Cred.

Assume that Y is the amount incurred (at end) and D is the % reported (in the example at 12 months). And ASSUMEthat these are independent.

So the amount at 12 months, X = D*Y (%Rep*ultimate). so D = X/Y; Sure. Good.

Now in the example:

E(Y) = 35m. Std(Y) = 10m. E(D) = E(X/Y) = .3. Std(D) = .20

I'm skipping the VHM, which you understand.

EVPV = E(VAR(X|Y)) = E(VAR(D*Y|Y=y)). So, if you know Y (as given), it's effectively a constant in the variance equation. Yielding:

E[(Y^2)*VAR(D)] = .2^2 * E(Y^2).... then you do the definition of variance turnaround to get the E(Y^2).

It REALLY helps me to put the equation into words, like VAR(X|Y) is the variance of the AMOUNT reported at 12months, knowing that the ultimate amount is Y. But I know that the amount at 12 months is a function of the Ultimate * the percent reported. So my only variable for the VARIANCE is the percent reported.

I hope I'm on the right track.

[The Sad Man]

Good job, KidCA. I was stuck on the jump the All10 solution made also. Wish they could have provided a more detailed solution.

[Sox34]

is there a situation/possible problem where you would ever need to use the info about "before cap elimination"?

[Examinator]

In this type of question, no. It's there to fill the page and mess with you.

[Sox34]

In this type of question, no. It's there to fill the page and mess with you.

lol that's what i figured