Actuarial Outpost Quick question about Limited Fluctuation Credibility theory
 User Name Remember Me? Password
 Register Blogs Wiki FAQ Calendar Search Today's Posts Mark Forums Read
 FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

 Enter your email to subscribe to DW Simpson weekly actuarial job updates. li.signup { display: block; text-align: center; text-size: .8; padding: 0px; margin: 8px; float: left; } Entry Level Casualty Health Life Pension All Jobs

 General Actuarial Non-Specific Actuarial Topics - Before posting a thread, please browse over our other sections to see if there is a better fit, such as Careers - Employment, Actuarial Science Universities Forum or any of our other 100+ forums.

 Thread Tools Search this Thread Display Modes
#11
06-20-2018, 06:35 PM
 Duke of Chalfont Member SOA Join Date: Apr 2011 Posts: 38

Sorry, was asking about a case where your full credibility standard is 1,082 claims, you expect 500, but observe 1,500. Is the credibility there 100% or sqrt(500/1082) = 68%?

At any rate, I do get the impression that there is a subtle difference between how LFC is generally applied in a mortality or a P&C context, and likely one that makes sense given the circumstances.

Looking at the SOA's credibility practice notes from 2009 (https://www.soa.org/Files/Research/P...eory-pract.pdf ), actual deaths/lapses are used in the simplified LFC formula on page I.6. That follows from an assumption that the deaths/lapses are Poisson distributed. However, there is an underlying assumption there that the true actual-to-expected ratio is that observed, instead of assuming it is just 100%.
#12
06-20-2018, 06:39 PM
 Duke of Chalfont Member SOA Join Date: Apr 2011 Posts: 38

Quote:
 Originally Posted by Colymbosathon ecplecticos Oh, and 1,082 isn't an arbitrary number.
Agreed. It is a number that follows from some rather arbitrary assumptions and inputs but that still works quite well in practice.
#13
06-20-2018, 07:17 PM
 Colymbosathon ecplecticos Member Join Date: Dec 2003 Posts: 5,964

Quote:
 Originally Posted by Duke of Chalfont Sorry, was asking about a case where your full credibility standard is 1,082 claims, you expect 500, but observe 1,500. Is the credibility there 100% or sqrt(500/1082) = 68%?
Yes, 68%.
Quote:
 Looking at the SOA's credibility practice notes from 2009 (https://www.soa.org/Files/Research/P...eory-pract.pdf ), actual deaths/lapses are used in the simplified LFC formula on page I.6. That follows from an assumption that the deaths/lapses are Poisson distributed. However, there is an underlying assumption there that the true actual-to-expected ratio is that observed, instead of assuming it is just 100%.
Think about it this way:

You expected your full credibility standard is 1082, and you expected 0.001 deaths (your risk set was 1 life for one year with q=0.001). Oops! He dies.

So your unweighted estimate for q is q=1.0 (I agree with this.)

Your credibility should be sqrt(0.001/1082) which is about 0.001.

Using actual, we'd get sqrt(1/1082) which is about 0.03.

The credibility weighted estimate is 1(0.001) + 0.001(0.999) = 0.00196

Your estimate would be 1(0.03) + 0.001(0.97) = 0.03137

=============

Also, from a regulator's point of view, your method fails to give the insured credit for good experience and doubly punishes bad experience. That is unfairly discriminatory.
__________________
"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."
#14
06-21-2018, 01:39 AM
 Duke of Chalfont Member SOA Join Date: Apr 2011 Posts: 38

Thanks, that helps. Though I do not think I agree with the conclusion from that example itself.

What I was clearly missing, and I am not sure how (guess it has been way too long since I saw anything P&C), is that the the A/E's you are talking about in P&C are loss ratios or whatever, not actual versus expected claims counts. Presumably, the expected # of claims are a better (or at least a fairer and more consistent) indicator of the "stability" of the observed loss ratio than the actual # of claims, and thus the preferred base to use for the credibility standard.

But when talking about mortality experience, the A/E's are the actual to expected deaths counts (potentially weighted, but can ignore that here). So, all else equal, more observed deaths really do mean a more stable observed A/E ratio in the LFC sense. If the expected deaths are 1000 but you observe 800, then the probability that the A/E is within a 5% relative tolerance of the estimate of 80% is about 84%, while with 1200 observed deaths that probability (around the 120% estimate) is 92% (if 1,082 deaths were required for full credibility, then the probability of the estimate being within a 5% tolerance would need to be above 90%). If we were focusing directly on the mortality rate, the conclusion would be the same.

With the example with 1 death, is the point supposed to be that the estimate of 0.03137 is too high? It probably is, but all sorts of assumptions (certainly Poisson, and even normality) breakdown with so few lives (1 in this case), so I am not sure I see any relevance.

Quote:
 Originally Posted by Colymbosathon ecplecticos Also, from a regulator's point of view, your method fails to give the insured credit for good experience and doubly punishes bad experience. That is unfairly discriminatory.
I (now) see that from a P&C perspective, but similar concepts certainly do not necessarily carry over to a mortality application. For example, in the context of pricing an annuity purchase for a pension plan partially using its own experience, using expected deaths could be seen to be potentially overcharging groups with higher-than-average mortality (insufficient credibility placed on their experience given the relative "stability") and also potentially overcharging ones with lower-than-average mortality (too much emphasis placed on their inherently less "stable" experience). A single premium will be paid in this case, so no chance to adjust given future experience. But again, this all follows from more observed deaths leading much more directly into the "stability" of the A/E's or mortality rates.

This was really quite interesting. I never had thought about the practical considerations of credibility in P&C or how it differs from the mortality applications with which I have at least some familiarity. Though I do promise to stay out of P&C-related threads in the future!

 Thread Tools Search this Thread Search this Thread: Advanced Search Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off

All times are GMT -4. The time now is 04:43 PM.

 -- Default Style - Fluid Width ---- Default Style - Fixed Width ---- Old Default Style ---- Easy on the eyes ---- Smooth Darkness ---- Chestnut ---- Apple-ish Style ---- If Apples were blue ---- If Apples were green ---- If Apples were purple ---- Halloween 2007 ---- B&W ---- Halloween ---- AO Christmas Theme ---- Turkey Day Theme ---- AO 2007 beta ---- 4th Of July Contact Us - Actuarial Outpost - Archive - Privacy Statement - Top

Powered by vBulletin®
Copyright ©2000 - 2018, Jelsoft Enterprises Ltd.
*PLEASE NOTE: Posts are not checked for accuracy, and do not
represent the views of the Actuarial Outpost or its sponsors.
Page generated in 0.18721 seconds with 11 queries