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  #201  
Old 12-05-2019, 08:26 AM
lostatsea lostatsea is offline
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There were no major changes to the syllabus, right? Planning to start studying in the new year.
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  #202  
Old 12-05-2019, 09:01 AM
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There were no major changes to the syllabus, right? Planning to start studying in the new year.
The only change I have seen is an errata for Taylor being added. Everything else seems to be identical.
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  #203  
Old 12-06-2019, 08:12 PM
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Clark, page 53, the information matrix

The notations are misleading, shouldn't "?" be theta, and "y" be i? I have no idea why they use a different set of notations here.
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  #204  
Old 12-11-2019, 07:44 AM
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Clark, page 53, the information matrix

The notations are misleading, shouldn't "?" be theta, and "y" be i? I have no idea why they use a different set of notations here.
Yes.
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  #205  
Old 12-11-2019, 10:33 AM
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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]
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Old 12-11-2019, 01:49 PM
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Yes.
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  #207  
Old 12-11-2019, 02:21 PM
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Mack 1994 is bothering me.

on pg.112, Mack states

The fact that the chain ladder estimator uses weights which are proportional to ��jk therefore means that ��jk is assumed to be inversely proportional to ������(Cj,k+1/Cjk|Cj1,...,Cjk)

I don't get how he came up with this conclusion. Why does the weight in the CL estimator imply Cjk is inversely proportional to the variance of the future development factor?
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  #208  
Old 12-11-2019, 02:36 PM
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Mack 1994 is bothering me.

Why does the weight in the CL estimator imply Cjk is inversely proportional to the variance of the future development factor?
Each variance assumption yields a different minimum variance unbiased estimator of f. For the basic variance assumptions, (constant, proportional, proportional to the square) the MVUE for each can be written with a similar formula, just by changing the weights.

So if you use a formula with a certain set of weights, you are implicitly making a statement about what you believe the variance relationship is (because if you believed it was something else, you are stupid for not using the MVUE for what you thought it was).
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Old 12-11-2019, 02:48 PM
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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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  #210  
Old 12-11-2019, 08:25 PM
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Quote:
Originally Posted by trueblade View Post
Mack 1994 is bothering me.

on pg.112, Mack states

The fact that the chain ladder estimator uses weights which are proportional to ��jk therefore means that ��jk is assumed to be inversely proportional to ������(Cj,k+1/Cjk|Cj1,...,Cjk)

I don't get how he came up with this conclusion. Why does the weight in the CL estimator imply Cjk is inversely proportional to the variance of the future development factor?
It's derived in appendix B
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