PDA

View Full Version : Brosius Question on Bayesian Method

AdoubledotAngleN
05-28-2007, 01:32 PM
First off, I am getting started early because I am busy with family stuff most of the month of October. Just wanted to establish that before I caught a bunch of crap for starting so early.:swear:

I was wondering if anyone knew where the Bayesian EVPV estimate comes from. It is probably right in front of me but I can't find it. It is on p15 in Loss Development using Credibility. It looks like this:

EVPV = E(VAR(X|Y)*Y^2)
SpeakLife!
05-28-2007, 02:09 PM
I was wondering if anyone knew where the Bayesian EVPV estimate comes from. It is probably right in front of me but I can't find it. It is on p15 in Loss Development using Credibility. It looks like this:

EVPV = E(VAR(X|Y)*Y^2)
first, note that you have not written the formula as presented on page 15. the formula Brosius is using is EVPV=E(Var(X/Y)*Y^2), not E(Var(X|Y)*Y^2). he uses the ratio X/Y, not the conditional variable X|Y.

now, looking at the footnote at the bottom of page 15, we see the curious assumption that both the mean and standard deviation of X/Y (not X|Y) do not depend on Y. this seems to suggest that E(X/Y)=E(X)/Y and Var(X/Y)=Var(X)/Y^2. could be wrong, though.

EVPV then equals E(Var(X/Y)*Y^2)=E(Var(X)/Y^2*Y^2)=E(Var(X)).
VHM then equals Var(E(X/Y)*Y)=Var(E(X)/Y*Y)=Var(E(X)).

again, might have messed something up somewhere.
AdoubledotAngleN
05-29-2007, 11:47 AM
first, note that you have not written the formula as presented on page 15. the formula Brosius is using is EVPV=E(Var(X/Y)*Y^2), not E(Var(X|Y)*Y^2). he uses the ratio X/Y, not the conditional variable X|Y.

now, looking at the footnote at the bottom of page 15, we see the curious assumption that both the mean and standard deviation of X/Y (not X|Y) do not depend on Y. this seems to suggest that E(X/Y)=E(X)/Y and Var(X/Y)=Var(X)/Y^2. could be wrong, though.

EVPV then equals E(Var(X/Y)*Y^2)=E(Var(X)/Y^2*Y^2)=E(Var(X)).
VHM then equals Var(E(X/Y)*Y)=Var(E(X)/Y*Y)=Var(E(X)).

again, might have messed something up somewhere.



Ok this makes a lot more sense. Thank you!