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  #11  
Old 02-13-2018, 12:27 PM
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I think this might be rule-of-thumb worthy AT BEST. I do not believe it to be true in all cases.
Think of it more in terms of it being a generalization that completely glosses over the complications of limited data.

What I described is one possible rule of thumb for working with layers where there are sufficient data. I like it for the reasons previously stated, but you could approach the task from a different direction and achieve acceptable results, as long as the inherent assumptions made along the way are consistent with the approach you're taking.

Once you start working with layers where data become too thin to be really usable, other techniques and judgment start coming into play. The details will depend on the application, what other data are available, etc. That's the fun part of the work, in other words.
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Old 02-13-2018, 05:47 PM
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To the OP.


You cannot directly derive usable excess loss development patterns from ground up loss development triangles.
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Old 02-14-2018, 10:09 AM
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I'm assuming two "appropriate" LDF sets that are from development data limited at $250k and $500k.

My feeling is that this approach might still understate IBNR in an excess layer because the portion of loss that exceeds $250k might develop more slowly on average than the the limited data does on average. Any thoughts?
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Old 02-14-2018, 01:05 PM
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I'm assuming two "appropriate" LDF sets that are from development data limited at $250k and $500k.

My feeling is that this approach might still understate IBNR in an excess layer because the portion of loss that exceeds $250k might develop more slowly on average than the the limited data does on average. Any thoughts?
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Old 02-14-2018, 01:24 PM
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I'm assuming two "appropriate" LDF sets that are from development data limited at $250k and $500k.

My feeling is that this approach might still understate IBNR in an excess layer because the portion of loss that exceeds $250k might develop more slowly on average than the the limited data does on average. Any thoughts?
That's correct.

If you have the data (your own or industry), one way to address this would be to develop an expected distribution of loss by size of loss for the subject book, factoring in trend, limits, and attachment points of the underlying data.

Given trended, developed capped losses, you can use that distribution to calculate expected uncapped or expected excess losses.

Coming up with such a distribution can, however, be a bit of a challenge.
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Old 02-14-2018, 03:18 PM
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I'm assuming two "appropriate" LDF sets that are from development data limited at $250k and $500k.

My feeling is that this approach might still understate IBNR in an excess layer because the portion of loss that exceeds $250k might develop more slowly on average than the the limited data does on average. Any thoughts?
Well to me that assumption sounds suspect. If you have two sets of LDFs, then they must have been derived from two loss triangles. If you have two triangles, then difference those and you have an excess triangle from which to derive link ratios. I'd prefer to do this then differencing the two sets with squared triangles, because I'd get a better view of the volatility on the excess triangle.

In your second paragraph change the word "might" to "should" and then I'm in agreement. I'm old so I learned this topic from a paper about excess LDF's by Pinto & Gogol, and a series of axioms from a textbook by Ruth Salzmann. I don't know what CAS material teaches the topic currently. The over-riding tendencies are straightforward. People (attorneys) do not drag out the adjudication of $10,000 claims for years and years. They do drag out $Million dollar - plus claims for years and years. Any claim that is open might develop upward. So the development that happens in late years generally is coming from the biggest claims.

Then there is the tail factor problem. It would be incorrect to assume that if your first dollar loss development triangle shows completion (or even redundancy!) as of X months then your excess development is complete at x months. This is a mistake often made by "pricers" (buyers, brokers, mga's, newbies) of excess layers that a seasoned, actuarially-trained practitioner is not likely to make. Does this make sense? If not I can give an example.
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Old 02-16-2018, 10:16 AM
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Well to me that assumption sounds suspect. If you have two sets of LDFs, then they must have been derived from two loss triangles. If you have two triangles, then difference those and you have an excess triangle from which to derive link ratios. I'd prefer to do this then differencing the two sets with squared triangles, because I'd get a better view of the volatility on the excess triangle.

In your second paragraph change the word "might" to "should" and then I'm in agreement. I'm old so I learned this topic from a paper about excess LDF's by Pinto & Gogol, and a series of axioms from a textbook by Ruth Salzmann. I don't know what CAS material teaches the topic currently. The over-riding tendencies are straightforward. People (attorneys) do not drag out the adjudication of $10,000 claims for years and years. They do drag out $Million dollar - plus claims for years and years. Any claim that is open might develop upward. So the development that happens in late years generally is coming from the biggest claims.

Then there is the tail factor problem. It would be incorrect to assume that if your first dollar loss development triangle shows completion (or even redundancy!) as of X months then your excess development is complete at x months. This is a mistake often made by "pricers" (buyers, brokers, mga's, newbies) of excess layers that a seasoned, actuarially-trained practitioner is not likely to make. Does this make sense? If not I can give an example.
Deep Purple, no example needed; this is exactly what I was thinking. Thanks for this.
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