Actuarial Outpost SOA #65
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 Short-Term Actuarial Math Old Exam C Forum

#1
05-20-2018, 11:42 PM
 RockOn Member SOA Join Date: Dec 2013 Studying for Exam C Favorite beer: Polygamy Porter Posts: 83
SOA #65

Hello!
A quick question about Non-Poisson frequency and classical credibility:

For this question I tried to use the following formula from the ASM manual table: 42.1

n0 * ((Var(n)/E[N]) + (Var(s)/(E[x]^2))

Where N represents frequency and x represents severity. However the SOA solution uses another formula to get the full credibility value:

n0 * (Var(S))

Where:
Var(s) = E[N] * Var(x) + Var(N) * (E[x])^2

Can someone explain why the second formula be used and not the first to calculate the full credibility value? Is there something in the wording of the problem?

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#2
05-21-2018, 10:50 AM
 Jim Daniel Member SOA Join Date: Jan 2002 Location: Davis, CA College: Wabash College B.A. 1962, Stanford Ph.D. 1965 Posts: 2,688

This is the danger in memorizing a bunch of different formulas for the full credibility standard for different cases---you get confused about which to use where.

For full credibility for a random variable W, the minimum number of _observations_ of W for full credibility is

(y / k)^2 Var[W] / E[W]^2.

In #65, my W is aggregate severity (denoted by X in the problem), and you have 2500 observations of the value of aggregate severity.

The formula you were applying inappropriately is for the minimum (expected) number of claims for full credibility for aggregate severity rather than for the minimum number of observations of aggregate severity.
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#3
05-22-2018, 11:50 AM
 RockOn Member SOA Join Date: Dec 2013 Studying for Exam C Favorite beer: Polygamy Porter Posts: 83

Yes, that is a subtlety that was lost on me.

I was thinking about the 2500 - not as observations but as exposures...

I think I need to study this further as I'm not sure I fully understand it yet.

Thank you again!
__________________
EXAMS: P | FM | MFE | MLC | STAM | PA |
VEE: ECON | STATS | CORP FINANCE |
FAP: MOD 1| MOD 2| MOD 3| MOD 4| MOD 5| IA| MOD 6| MOD 7| MOD 8| FA |
#4
05-22-2018, 12:07 PM
 Jim Daniel Member SOA Join Date: Jan 2002 Location: Davis, CA College: Wabash College B.A. 1962, Stanford Ph.D. 1965 Posts: 2,688

Quote:
 Originally Posted by RockOn Thank you for the reply! Yes, that is a subtlety that was lost on me. I was thinking about the 2500 - not as observations but as exposures... I think I need to study this further as I'm not sure I fully understand it yet. Thank you again!
That basic formula always gives you the minimum number of observations of W. You just have to ask yourself “when do I observe a value of W?” When W is frequency or aggregate severity per exposure unit, the answer is “every time an exposure unit goes by”. When W is severity per accident, the answer is “every time an accident occurs”.
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Jim Daniel
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