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Old 12-11-2019, 02:48 PM
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trueblade trueblade is offline
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Quote:
Originally Posted by AbedNadir View Post
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[Y|X] = (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) = (5-4)*0.9+10 =10.9
Reserve: L(x) - x = 10.9-5=5.9 < 6, hence the decrease
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