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actuarialista
02-21-2011, 10:52 AM
At the bottom of page 161, Werner & Modlin state several formulas for Indicated Differential Change, including

\frac{\frac{(L+E_L)_i}{P_{I,i}}}{\frac{(L+E_L)_B}{ P_{C,B} }.

I went through the process of obtaining this formula, and my problem is that I can't figure out where the P_{I,i}
came from. To me it looks like it should be P_{C,i} instead, because it comes from X_i \bar{P_{C,i}} .

Any thoughts on this?

Vorian Atreides
02-22-2011, 10:05 AM
I agree that the exposition isn't clear and needs to be addressed/corrected. However, I offer the following for the use of P_{\small{I},i} in the formula:

Consider that P_{\small{I},i} is (almost) the same as P_{\small{C},i}, except that it's already adjusted by the (statewide) indicated change.

For example, suppose that the target loss ratio is 65%, but the actual loss ratio is 61%. This indicates an overall decrease of 6.15%. So,

P_{\small{I},i} = P_{\small{C},i}\; \times\; $$\, 1\; +\; (-0.0615)\,$$

When we simply decrease the base rate by 6.15%.

Much of the material in this chapter centers around making changes to specific classifications that are revenue neutral--which would be the case if we do the above.

However, with this being stated, one would, then, need to use P_{\small{I, B}} in the denominator to be consistent. However, I think the simplest solution would be retaining the use of P_{\small{C},i}.

chopsuey
02-22-2011, 10:36 AM
I think you might be right -- P_I,i would be (P_C,i x Ind Chg Factor) which is not what is used in the calculation of the Indicated Differential Change.

chopsuey
02-22-2011, 10:37 AM
didn't refresh page after VAs post. "you" above refers to OP.

actuarialista
04-01-2012, 06:40 PM
At the bottom of page 161, Werner & Modlin state several formulas for Indicated Differential Change, including

\frac{\frac{(L+E_L)_i}{P_{I,i}}}{\frac{(L+E_L)_B}{ P_{C,B} }.

I went through the process of obtaining this formula, and my problem is that I can't figure out where the P_{I,i}
came from. To me it looks like it should be P_{C,i} instead, because it comes from X_i \bar{P_{C,i}} .

Any thoughts on this?

Bumping my own post because it looks like this was indeed an error in Werner & Modlin, that was corrected on Jan. 4th, 2012. See "Exam 5" section of http://casact.org/admissions/syllabus/index.cfm?fa=update#exam5 Note that what was on p. 161 (in the old edition I had) is now on p. 165.