April 2015 Question 3

[Chaya Baheti]

Question -
An actuary has calculated the expected ultimate claims on a book of general insurance business using the chain ladder method on both a paid and incurred basis. He notes that the amounts which he projects on a paid basis are significantly higher than those he has projected on an incurred basis. Further inspection shows that this effect is common across all accident years and is not due to a single unusual early payment; the actuary has had the calculations and data fully checked.
(i) Suggest two main reasons why this phenomenon might have arisen. [2

Solution-

One possible explanation for this is that claim payments may have speeded up. This may be caused by either a change in the rate at which the gross claim payments are made, or, if we are projecting net data, by a change in the rate at which reinsurance recoveries are received.
Therefore, if an average payment pattern is being used which is based on the historical rate at which claims have been paid it will tend to over-estimate the ultimate claim amounts for the more recent accident years.
Another possibility is that there has been a reduction in the overall level of reserves being established for outstanding claims (ie case reserve prudence).
Therefore, if an average incurred claims pattern is being used which is based on the historical rate at which claims have been reported it will tend to under-estimate the ultimate claim amounts for the more recent accident years.

I did not quite understand this. Cna someone please explain with example

 

[Ian Senator]

You will follow it better if you can put an example together yourself. Create a triangle of paid claims, and perform a BCL on it. Then speed up the paid claims in the most recent years (ie make the numbers in the early columns but later rows bigger more quickly) and do another BCL. See what happens. Do the same with an incurred claims triangle, making sure your incurred claims in each cell are at least as big as your corresponding paid claims.

 

[Chaya Baheti]

So, I tried doing it and for last two AYs my ultimate claim did appear to be higher.

But I want to clear my conceptual doubt.. I am not from a reserving background and these problems are actually making me question everything.

1st thing - is it general that incurred data would give higher ultimate claims than paid data because incurred data has paid + case estimates
2nd thing - when I increase my payments for two AYS my ldfs and cdfs have decreased for that year symbolising faster development
but it can be due to other reasons such as claim amounts have increased or more number of claims are coming in, isnt it. I agree that then it would have also impacted the incurred data

3rd thing - if the effect is common across all AYs then why do we assume that claim settling have increased in recent years

4th - "Therefore, if an average payment pattern is being used which is based on the historical rate at which claims have been paid it will tend to over-estimate the ultimate claim amounts for the more recent accident years." what ds historical rate and average payment pattern signifies here the one that I just adjusted but that would be a new thing, right as claims have speeded up recently so average pattern should signify normal claims

 

[Chaya Baheti]

Similarly I came across this in one of the questions in similarlines - "Another consideration will be the treatment of large losses both in the claim numbers triangle and also in the average costs. It is likely that large claims are reported at a different rate to the attritional claims (ie quicker), so by not allowing for this we may overestimate the pure IBNR component." and I have hard time understanding this too

 

[Katherine Young]

Without knowing which question you're looking at, it's hard to give an answer out of context. However, I can try:

Let's imagine you have derived your chain ladder profile from (slower) attritional claims. Slow development implies a relatively low % developed.

Now imagine that your most recent year contains large losses. These develop more quickly than attritional claims, so your position-to-date is already quite advanced. Hence, you want to apply a relatively high % developed - not the % implied by the chain ladder.

So hopefully you can see that your chain ladder will overstate ultimate claims.

If you're still not sure, try plugging a few numbers into a spreadsheet and see what happens.