Actuarial Outpost Quick question about Limited Fluctuation Credibility theory
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#1
06-20-2018, 02:07 PM
 Gods_Dice Member SOA Join Date: Nov 2011 Posts: 202
Quick question about Limited Fluctuation Credibility theory

In determining Z, do you have to use the expected count, or can you use the actual count? I remember it being expected, but I have a spreadsheet here where the spreadsheet owner used actual. Is that acceptable?

For instance:

34 actual claims vs. 57 expected claims.

Actual A/E is 59% and the original assumption we are looking to adjust is 97%.

The spreadsheet calculates Z as sqrt(34/1082) = 18%

So the potential new value is ((1-.18) * 97%) + (.18 * 59%) = 90%.

Is this acceptable? Or should Z instead be sqrt(57/1082) = 23%? This would obviously change the potential new value slightly.

Thanks.
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#2
06-20-2018, 02:12 PM
 Colymbosathon ecplecticos Member Join Date: Dec 2003 Posts: 5,965

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#3
06-20-2018, 02:18 PM
 Gods_Dice Member SOA Join Date: Nov 2011 Posts: 202

Quote:
 Originally Posted by Colymbosathon ecplecticos Suppose that you observed 0 instead of 34. Does that answer your question?
Great point. I thought it looked wrong, just wanted to make sure I wasn't missing something because the guy who put this together is usually pretty sharp.

Thanks again.
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#4
06-20-2018, 04:19 PM
 Duke of Chalfont Member SOA Join Date: Apr 2011 Posts: 38

To be clear:
With 0 observed claims you would apply 0% credibility. It should be actual.
#5
06-20-2018, 05:16 PM
 Colymbosathon ecplecticos Member Join Date: Dec 2003 Posts: 5,965

Quote:
 Originally Posted by Duke of Chalfont To be clear: With 0 observed claims you would apply 0% credibility. It should be actual.

If you know the expected number of claims, as is the case in the OP, then use it. The full credibility standard was presumably computed using this estimate.

If you don't know it, estimate it the best that you can. The observed number is such an estimate.
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"What do you mean I don't have the prerequisites for this class? I've failed it twice before!"

"I think that probably clarifies things pretty good by itself."
#6
06-20-2018, 05:22 PM
 Marcie Member CAS Join Date: Feb 2015 Posts: 8,852

Quote:
 Originally Posted by Colymbosathon ecplecticos Think about this. It makes no sense. If you know the expected number of claims, as is the case in the OP, then use it. The full credibility standard was presumably computed using this estimate. If you don't know it, estimate it the best that you can. The observed number is such an estimate.

The theory is based on expected. Sometimes the best estimate of expected is actual.
#7
06-20-2018, 05:58 PM
 Duke of Chalfont Member SOA Join Date: Apr 2011 Posts: 38

Hmmm, perhaps I didn't think things through as I have usually seen actual used in practice (mostly in a mortality context).

But how does the expected relate to the full credibility standard? Obviously in this case the 1,082 was just set arbitrarily in effect. If you have 1,500 actual claims but only expected 500, would you still apply partial credibility? Seems counterintuitive to me to apply partial credibility there, but again I am approaching this from a mortality context. 0 deaths gets 0 credibility no matter what the expected is in my books, but mortality is different in that the actual and expected are not likely to be very far off.
#8
06-20-2018, 06:10 PM
 Colymbosathon ecplecticos Member Join Date: Dec 2003 Posts: 5,965

If your full credibility standard is 500 claims and you expect 1500, then you have achieved full credibility and Z=1. Z is always between 0 and 1.

You are correct that the expected (total) number of claims is not used in computing the full credibility standard. The expected number of claims per exposure is typically used to give a measure of the full credibility standard in exposure units. Typically, car-years for auto insurance and life-years for human mortality.
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#9
06-20-2018, 06:12 PM
 Colymbosathon ecplecticos Member Join Date: Dec 2003 Posts: 5,965

Oh, and 1,082 isn't an arbitrary number.
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"What do you mean I don't have the prerequisites for this class? I've failed it twice before!"

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#10
06-20-2018, 06:14 PM
 Colymbosathon ecplecticos Member Join Date: Dec 2003 Posts: 5,965

Quote:
 Originally Posted by Duke of Chalfont 0 deaths gets 0 credibility no matter what the expected is in my books, but mortality is different in that the actual and expected are not likely to be very far off.
Translation:

Yeah, we expected 500,000 of these million people to die this year, but not one of them did!

Okay, leave our best estimate at q=0.5.
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