Actuarial Outpost
 
Go Back   Actuarial Outpost > Actuarial Discussion Forum > Property - Casualty / General Insurance
FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions


Upload your resume securely at https://www.dwsimpson.com
to be contacted when our jobs meet your skills and objectives.


Reply
 
Thread Tools Search this Thread Display Modes
  #1  
Old 10-20-2008, 02:09 PM
Gareth Keenan's Avatar
Gareth Keenan Gareth Keenan is offline
Member
CAS
 
Join Date: Feb 2006
Location: Garden State
Studying for #9
Favorite beer: butter
Posts: 1,300
Default Topic: Pros/Cons on a tail factor selection techinique?

So, I have seen a technique for selecting a tail factor while at work, that I'd like to get others opinions on. This is really only applicable for mid to long tail lines.

So, let's say you are looking at a line of business, say general liability for example, and you have developed your triangles, and made a tail factor selection on a cumulative incurred triangle. Next up would be your triangle squaring on a cumulative paid basis. What I have seen done, is to select a tail factor on a paid basis, so that it reconciles your ultimate paid claims to ultimate incurred claims.

For example, lets say that on an incurred basis, you have data back to accident year 1999. So, after the incurred triangle squaring you've got for 1999, 2000, and 2001 ultimate loss of 20,000; 22,000; and 25,000 respectively, for a total incurred loss for 99-01 of 67,000. Then we move to our paid basis. Let's say then, for 1999, 2000, and 2001 the ultimate loss is projected to be (before the application of a tail factor, but after applying the other ATA factors) 19,500; 23,000; and 22,000. The technique is designed to match your paid loss to your incurred loss. In this case the tail factor on a paid basis would be

While the above situation is one example, what are the pros and cons to using this technique in general?

Regards, and Happy Monday(if that isn't an oxymoron to you)

Gareth Keenan
Reply With Quote
  #2  
Old 10-20-2008, 02:23 PM
great3981's Avatar
great3981 great3981 is offline
Member
CAS AAA
 
Join Date: Nov 2003
Studying for nothing, ever ever again
Posts: 1,363
Default

The technique you describe is called "balancing the tails". It is highly recommended for the reasons to which you allude, namely that the Paid and Incurred loss development methods converge to same/similar answers.

A more sensitive part of the analysis is to select the incurred tail factor, but it is often easier to select an incurred tail factor than a paid tail factor. Balancing the tails makes your assumptions consistent.
__________________
The wonderful thing about tiggers
Is tiggers are wonderful things!
Their tops are made out of rubber;
Their bottoms are made out of springs!
They're bouncy, trouncy, flouncy, pouncy,
Fun! Fun! Fun! Fun! Fun!
But the most wonderful thing about tiggers is
I'm the only one!

Diversions Wins!:
Reply With Quote
  #3  
Old 10-20-2008, 03:14 PM
Gareth Keenan's Avatar
Gareth Keenan Gareth Keenan is offline
Member
CAS
 
Join Date: Feb 2006
Location: Garden State
Studying for #9
Favorite beer: butter
Posts: 1,300
Default

Thanks great3981,

Well perhaps this is a silly question but is it ever okay then for your paid and incurred methods to not agree? In what circumstances would you want different ultimate loss on a paid vs. incurred basis? I can see the benefit of not having to reconcile differences in ultimate loss projection until later, but I'm not certain if that is desirable in every instance.

Gareth Keenan
Reply With Quote
  #4  
Old 10-21-2008, 02:25 AM
great3981's Avatar
great3981 great3981 is offline
Member
CAS AAA
 
Join Date: Nov 2003
Studying for nothing, ever ever again
Posts: 1,363
Default

There are very few cases when I would not want my paid and incurred methods to at least converge. After all, you are trying to use each to determine the same number... estimated ultimate losses.

Upon reading your post and speculating a bit, I thought maybe if your incurred method is distorted by case reserve strengthening, you would rather see your paid method and your adjusted incurred method rather than your paid and incurred method converge. Most of the time, however, case reserve strengthening will only distort those accident years with a significant amount of development left, which is normally not in the tail.

I do emphasize that we would ideally have the paid and incurred methods converge for all years but "balancing the tail" is appropriate only for the earliest few years (I normally judge by the significance of the remaining case reserves). Other techniques/methods, such as BF type approaches, are used to smooth the later years.
__________________
The wonderful thing about tiggers
Is tiggers are wonderful things!
Their tops are made out of rubber;
Their bottoms are made out of springs!
They're bouncy, trouncy, flouncy, pouncy,
Fun! Fun! Fun! Fun! Fun!
But the most wonderful thing about tiggers is
I'm the only one!

Diversions Wins!:
Reply With Quote
  #5  
Old 10-21-2008, 02:22 PM
Morrison Morrison is offline
Member
 
Join Date: Jun 2002
Posts: 261
Default I see it differently

I have to say, I am having difficulty understanding why you would pick a paid loss tail LDF to make sure your paid loss ultimates match your incurred loss ultimates. It seems to defeat the very purpose of performing the second method.

It seems to me the whole idea of using a second development method (i.e. the paid method in this case) is to provide a reasonability check of your first method (the incurred in this case) and when the two methods produce materially different results, investigate why. If you select paid tail factors that produce the exact same answer as your incurred method, then why bother even performing the paid loss development? All you are doing is confirming your original incurred loss development ultimate estimate. You've really only performed one method. I can see how it makes life easier because you don't have to explain/investigate why the two methods produce different results, but that is the whole reason you perform more than one method, to test the consistency of your results.

The value of of the paid loss development method is to serve as a counter-balance to the incurred loss development method, implicity assuming that paid development patterns are unchanged by changes in case reserving practices and differences in your paid and incurred loss development ultimates reflect a change in either: a) case reserving practices or b) payment practices. By forcing the two to converge, you effectively lose this check and balance.
Reply With Quote
  #6  
Old 10-22-2008, 08:56 PM
UCSDKID UCSDKID is offline
Member
CAS
 
Join Date: May 2005
Location: Lansing, MI
Posts: 753
Default

Another method that can be used is to fit a decaying curve to the LDFs. I have used both an exponential and power curves to fit loss development at my job. They can be easily done in Excel.
Reply With Quote
  #7  
Old 10-23-2008, 11:13 PM
MountainHawk's Avatar
MountainHawk MountainHawk is offline
Member
CAS AAA
 
Join Date: Dec 2001
Location: Salem, MA
Studying for Nothing!!!!
College: Lehigh University Alum
Favorite beer: Yuengling
Posts: 64,850
Default

Quote:
Originally Posted by Morrison View Post
I have to say, I am having difficulty understanding why you would pick a paid loss tail LDF to make sure your paid loss ultimates match your incurred loss ultimates. It seems to defeat the very purpose of performing the second method.

It seems to me the whole idea of using a second development method (i.e. the paid method in this case) is to provide a reasonability check of your first method (the incurred in this case) and when the two methods produce materially different results, investigate why. If you select paid tail factors that produce the exact same answer as your incurred method, then why bother even performing the paid loss development? All you are doing is confirming your original incurred loss development ultimate estimate. You've really only performed one method. I can see how it makes life easier because you don't have to explain/investigate why the two methods produce different results, but that is the whole reason you perform more than one method, to test the consistency of your results.

The value of of the paid loss development method is to serve as a counter-balance to the incurred loss development method, implicity assuming that paid development patterns are unchanged by changes in case reserving practices and differences in your paid and incurred loss development ultimates reflect a change in either: a) case reserving practices or b) payment practices. By forcing the two to converge, you effectively lose this check and balance.
That's why you only balance it in the aggregate over 3 to 5 years, not for any particular year. This way, you have the same magnitude of tail, and the differences in indication are from what is seen in the triangles themselves, not because you've selected disparate tails.
__________________

Play in the AO Prediction Game now!



1
Reply With Quote
  #8  
Old 04-25-2018, 01:55 PM
behindthebag behindthebag is offline
Member
CAS
 
Join Date: Jul 2016
Favorite beer: Blue Moon (prefer single malt)
Posts: 40
Default

Quote:
Originally Posted by MountainHawk View Post
That's why you only balance it in the aggregate over 3 to 5 years, not for any particular year. This way, you have the same magnitude of tail, and the differences in indication are from what is seen in the triangles themselves, not because you've selected disparate tails.
Any chance that many years later you can elaborate a little on this? Specifically, the aggregate over 3 to 5 years part. I'm an EL doing tail factors at work and thinking through this right now.
Reply With Quote
  #9  
Old 04-25-2018, 03:26 PM
tommie frazier tommie frazier is offline
Member
 
Join Date: Aug 2003
Favorite beer: The kind with 2 e's
Posts: 22,926
Default

Quote:
Originally Posted by behindthebag View Post
Any chance that many years later you can elaborate a little on this? Specifically, the aggregate over 3 to 5 years part. I'm an EL doing tail factors at work and thinking through this right now.
you might have to try sending him a private message. Have not seen hawk around for a while
__________________
Removed a dated athletic reference under pressure from a friend. You can still give money to help fund research on neurofibromatosis (nf).

General info at www.ctf.org

Team donation page here.
Reply With Quote
  #10  
Old 04-25-2018, 03:51 PM
tometom's Avatar
tometom tometom is offline
Member
CAS AAA
 
Join Date: May 2004
Favorite beer: Homebrew
Posts: 13,011
Default

I believe he's just saying you aggregate the tail factor over multiple years. so for example if your paid/incurred ultimates are like this:
1999: 10,000/11,000
2000: 10,000/12,000
2001: 10,000/10,000
you don't apply an adjustment of 1.1 to 1999, 1.2 to 2000 and 1.0 to 2001, you combine them together and adjust all years by 1.1.
__________________
If I had some duct tape, I could fix that.
Reply With Quote
Reply

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

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 10:02 AM.


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 0.48067 seconds with 9 queries