Quote:
Originally Posted by AbedNadir
Page 11 of Brosius, I'm looking at the linear approximation formula and the 1.2.3 listed for Hugh White's questions. If Cov(X,Y) < Var(X), isn't L(x) still bigger than E[Y]? How is this a decrease in the reserve? Isn't this true for all conditions?
Like, let's say x = 5 and E(X) = 4, then under all conditions E[YX] = (something bigger than 0 ) + E[Y]

Correct me if I'm wrong. I think the main point here is L(X) will increase less than the increase in x and they are comparing the following two reserves
Assume Cov(X,Y)/Var(X)=0.9, E[Y]=10
Expected reserve = E[Y]  E[X] = 10  4 = 6
Estimated Ultimate L(x) = (54)*0.9+10 =10.9
Reserve: L(x)  x = 10.95=5.9 < 6, hence the decrease