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#201
12-05-2019, 08:26 AM
 lostatsea Member CAS Join Date: Oct 2015 Posts: 64

There were no major changes to the syllabus, right? Planning to start studying in the new year.
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#202
12-05-2019, 09:01 AM
 Unrealistic Ace Member CAS Join Date: Nov 2017 Posts: 234

Quote:
 Originally Posted by lostatsea 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.
#203
12-06-2019, 08:12 PM

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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ACAS 7 8 9
#204
12-11-2019, 07:44 AM
 Unrealistic Ace Member CAS Join Date: Nov 2017 Posts: 234

Quote:
 Originally Posted by trueblade 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.
#205
12-11-2019, 10:33 AM
 AbedNadir Member CAS SOA Join Date: Mar 2014 Studying for FCAS Posts: 2,848

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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Last edited by AbedNadir; 12-11-2019 at 10:36 AM..
#206
12-11-2019, 01:49 PM

Quote:
 Originally Posted by Unrealistic Ace Yes.
Ty!
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ACAS 7 8 9
#207
12-11-2019, 02:21 PM

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?
Attached Images

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ACAS 7 8 9
#208
12-11-2019, 02:36 PM
 CuriousGeorge Member CAS SOA Join Date: Dec 2005 Posts: 1,629

Quote:
 Originally Posted by trueblade 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).
#209
12-11-2019, 02:48 PM

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[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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ACAS 7 8 9
#210
12-11-2019, 08:25 PM
 AbedNadir Member CAS SOA Join Date: Mar 2014 Studying for FCAS Posts: 2,848

Quote:
 Originally Posted by trueblade 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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