CM2-21: Run-off triangles page 6

Hi. I think the issue might be with the statement "and if we know that there was an accident 2 years ago". How would we know unless it was reported? In which case it won't appear in the IBNR figure, because it's been reported.
Does this match with what you're asking?
Thanks
Steve

 

Hi
I'm afraid I'm still not entirely sure what the question is
If a claim is reported today (in 2021) for an accident which occurred two years ago (in 2019) then depending on how the run-off triangle is defined that claim amount will either sit in the 2021 or the 2019 row. It will appear in the 2021 row (Development Year 0) if we're using "reporting year" or in the 2019 row (Development Year 2) if we're using "accident year".
Remember that the numbers in the top-left triangle of the table represent the known claim amounts that have been paid. The question on page 6 has to do with reserves - which is the estimate of future claim payments.
Please let me know if this still doesn't help and I'll ask someone else to chip in to the conversation.
Thanks
Steve

 

Hi

A numerical example might help. Consider an insurance contract where 90% of claims are reported in the first year and 10% of claims are reported in the second year. All claims are for an amount of 100, but 50% of this is paid in the year of notification and 50% in the year after.

Let's say that there are 20 claims in 2018, 30 in 2019 and 40 in 2020.

Let's first look at accident year. The run off triangle for the incremental claims then looks like this (with commas between the various entries)

2018 20 x 0.9 x 0.5 x 100, 20 x 0.9 x 0.5 x 100 + 20 x 0.1 x 0.5 x 100, 20 x 0.1 x 0.5 x 100
2019 30 x 0.9 x 0.5 x 100, 30 x 0.9 x 0.5 x 100 + 30 x 0.1 x 0.5 x 100
2020 40 x 0.9 x 0.5 x 100

this gives:

2018 900, 1,000, 100
2019 1,350, 1,500
2020 1,800

We'll then make these numbers cumulative and work out the ratios to project the missing values. This will give us the reserve for the outstanding claim payments and the IBNR for the accident years 2019 and 2020. The IBNR will be included for 2020 as we can see in the table that the second and third delay years for 2018 have also included the claims from 2018 that were notified late.

Let's now look at reporting year. We now put the 10% of claims incurred in 2018 that are reported late into the 2019 reporting year. So the run off triangle for the incremental claims now looks like this

2018 20 x 0.9 x 0.5 x 100, 20 x 0.9 x 0.5 x 100, 0
2019 30 x 0.9 x 0.5 x 100 + 20 x 0.1 x 0.5 x 100, 30 x 0.9 x 0.5 x 100 + 20 x 0.1 x 0.5 x 100
2020 40 x 0.9 x 0.5 x 100 + 30 x 0.1 x 0.5 x 100

this gives:

2018 900, 900, 0
2019 1,450, 1,450
2020 1,950

We'll then make these numbers cumulative and work out the ratios to project the missing values. This will give us the reserve for the outstanding claim payments but not the IBNR for the accident years 2019 and 2020. We can see that the 2020 projected numbers will be only 1950 and 0 for the second and third years, so will only include the claims reported so far and will miss the 4 claims reported late.

I'll leave it as an exercise for you to complete the triangles and calculate the reserves. You'll see that the reserve calculated using the reporting year triangle is smaller than the reserve for the accident year triangle, the difference being the IBNR.

I hope this helps.

Best wishes

Mark