Actuarial Outpost Topic: Pros/Cons on a tail factor selection techinique?
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#1
10-20-2008, 01:09 PM
 Gareth Keenan Member CAS Join Date: Feb 2006 Location: A state that means good morning in Japanese Studying for Exam 9 Favorite beer: butter Posts: 1,094
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 $\frac{20,000+22,000+25,000}{19500+23,000+22,000} = 1.039$

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
#2
10-20-2008, 01:23 PM
 great3981 Member CAS AAA Join Date: Nov 2003 Studying for nothing, ever ever again Posts: 1,263

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.
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#3
10-20-2008, 02:14 PM
 Gareth Keenan Member CAS Join Date: Feb 2006 Location: A state that means good morning in Japanese Studying for Exam 9 Favorite beer: butter Posts: 1,094

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
#4
10-21-2008, 01:25 AM
 great3981 Member CAS AAA Join Date: Nov 2003 Studying for nothing, ever ever again Posts: 1,263

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.
__________________
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!:
#5
10-21-2008, 01:22 PM
 Morrison Member Join Date: Jun 2002 Posts: 244
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.
#6
10-22-2008, 09:25 PM
 AMMW Member CAS Join Date: Dec 2007 Posts: 924

Quote:
 Originally Posted by Morrison 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.
#7
10-23-2008, 10:13 PM
 MountainHawk Member CAS AAA Join Date: Dec 2001 Location: Salem, MA Studying for Nothing!!!! College: Lehigh University Alum Favorite beer: Yuengling Posts: 55,619

Quote:
 Originally Posted by Morrison 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.
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#8
10-22-2008, 07:56 PM
 UCSDKID Member CAS Join Date: May 2005 Location: Lansing, MI Studying for Exam 9 Posts: 741

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.

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