Sept 2004 Paper

I know this question has been asked before but I am still struggling to understand how they arrive at mid Sept for the first year average claim date.
This assumption gives equal weight to both tranches of business, but in terms of the earnings weights the first tranch is earnt of 10 months, and the second for 4 months. Therefore should the average date be (10/14)*1Aug + (4/14)*1Nov? Doing this I get about 25th August.

I also get this answer if I look at the exposure each month and assume an average claim date of half way (0.5 mid jan, 1.5 mid feb...11.5 dec) through each month. The weighted average gives 7.85, which is about 25th August.

I can understand why this is different to the solutions which give equal weight to both, but I am not clear if this method is wrong?

I also don't understand why the third method of just counting 7 units of expousre to get to mid Sept (see earlier forum) gives mid sept?

 

Hi,

For the first year, we are trying to find the average date of the claims occurring in that calendar year (2000).
We're told that the number of vehicles added each year is split evenly between March and September, so both tranches will get equal weight.

The first tranche is written on 1st March 2000. The claims arising from that business will occur any time between 1st March and 31st Dec - on average this is 1st August (10/2=5 months after 1st March).

The second tranche is written on 1st Sept 2000. The claims arising from that business will occur any time between 1st Sept and 31st Dec - on average this is 1st November (4/2=2 months after 1st Sept).

So, on average, claims arise mid-Sept (1/2*1st Aug + 1/2*1st Nov). The weighting is ½ and ½ because we have equal amounts of business for each. We wouldn't weight using the 10 and 4 because we've already allowed for that in the average claim dates.

[An alternative way of looking at this is to say that, of all the claims that occur in 2000, the first tranche contributes to claims happening from 1st March to 1st Sept and both tranches contribute to claims happening from 1st Sept to 31st Dec. So the weightings would be 1/3 and 2/3.
Considering when these claims happen, on average, gives:
1/3*1st June + 2/3*1st Nov = mid-Sept. ]


Coralie

 

Apologies but i am still not convinced by this.
I don't think the answer takes account for the difference in the amount of each tranche earnt. Yes they are written 50/50 but it that actual year tranche one is more exposed and so it's average claim date should have more weight.

If you take the 1/3 & 2/3 argument to the extreme and say the second tranche was only exposed to one month then that would say that you would give 2/3 weighting to just a single month of exposure. Basically saying that 2/3 of claims in that accident year are going to happen in that month!

I really think the answer is assuming that both tranches have the same amount of exposure in the year, when actually the first tranche is more exposed and should therefore be more likely to give rise to a claim.

 

What does 'assuming that there are no offs other than at end of year 3.' mean?