IBNER and Pure IBNER

[salman100]

Hi Everyone

This is regarding determining IBNER and Pure IBNR.

My understanding is below:

• the report cohort triangle will not give Pure IBNR. So it can be used to determine IBNER
• the usual accident year triangle will provided IBNR (ie IBNER and Pure IBNR)
• so in this way both IBNER and IBNR can be determined.

There was a question on this subject in ST7 - Sept 2017 exam.

In examiners report, the solution is:

• use ACPC method to determine the Pure IBNR
  • The claim count triangle is used to project the ultimate claims.
  • The ultimate ACPC and ultimate claims will give Pure IBNR
• then subtracting the above Pure IBNR from IBNR determined by accident year will give IBNER.

I think this is just a usual application of traditional ACPC method which give IBNR (ie pure IBNR and IBNER) and not just Pure IBNR.

What do you think about my approach and understanding?

Regards

 

[Ian Senator]

Your approach and understanding seem fine.
The examiner's solution probably assumes that the ACPC is simply the expected ultimate claim cost of any claim yet to come in, so when multiplied by the number of claims expected, gives pure IBNR. If the ACPC calculated was allowing for IBNER then you're right, it would give the pure+IBNER. The ACPC method is very broad and non-specific, so any reasonable interpretation would score, including yours.

 

[Francis Karua]

In my opinion pure IBNR is estimated by using the date of accident and the date of reporting for origin year and development year respectively when building the run-off triangles. This can be on either of the deterministic statistical models. On the other hand, IBNER is estimated by using the date of reporting and the date the claim is paid (whether full or partial) for the origin years and development years respectively. From my point of view, I usually see the IBNER as a reserve if it emerges that the company is under-reserving after performing an adequacy on the case estimates. Hope this ids clear. @Ian Senator Am I on the right track or lost altogether?

 

[Ian Senator]

I'm not quite sure what's being tabulated in your first example, Francis. But yes, in your second example (tabulating claims paid using a reporting year cohort), you will be able to calculate IBNER but not IBNR. As for your last point, don't forget that IBNER can also be negative (over-reserving) too.

 

[Francis Karua]

Thank you for the response Ian. The last statement is noted. The first example is for pure IBNR. It means the delay of reporting from the date of loss and date when the claim is reported e.g. most claims incurred in December are normally reported in the first quarter of the following year. Or how is it estimated?

 

[Ian Senator]

Oh, I think I see what you're saying now. What you describe sounds to me like a 'delay table' - whereby you analyse how long it usually takes for claims to be reported after they have happened. This is then used to predict how many claims are yet to be reported yet have already occurred. Then you multiply this by an ACPC for an IBNR claim.
This is a valid way of calculating IBNR, yes. It's different from Salman's suggestion of using an AY cohort in a BCL approach, which would give you pure IBNR+IBNER.

 

[Francis Karua]

Thank you for the response.

There is also a challenging question from A2015 Q6 (i) On the part of calculating the high and low ultimate claims using the ICL , PBF and ICF methods... The credibility formula for BF seems not to work

 

[Darren Michaels]

Francis as far as I am aware the BF formula works fine in that question. The full solution is set out in the ASET.