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Sept 2013 Q8 iii

P

pdf1987

Member
Hi

I think I'm missing something on this question...

To determine the exposure during the year, we have been given the following information:
Number of policies in force at the start of the year=288,280
Number of new written policies in year=19,000
Number of cancellations in year=9,000

My approach (which I was quite sure was wrong at the time) was to:
1. Assume policies were annual so all those in force at the start of the tear would expire at some point throughout the year (on average half way through)
2. Exposure from the above is therefore half of the policies in force at the start of the year on average
3. Then follow the same halving approach for new policies written and cancellations

The solution however takes the exposure to be 288,280 + (19,000 - 9,000)/2

Looking back at the question, I guess my question is why aren't the policies in force at the start of the year being halved to obtain the exposure? Is it because all of these policies are assumed to renew when they expire apart from the 9,000 cancellations and the 19,000 policies are new business on top of that?

I understood the details given as the cancellations being mid-term (not lapses at renewal) and the written policies in the year being 19,000 which I think is where I misunderstood. That would lead to a huge drop off in live policies at the end of the year!
 
I have some sympathy with you here, it's easy to see why you fell into this trap.

Let's not get too bogged down into which policies cancel, and which lapse at renewal etc. We'll just think about the concepts instead ...

What you did was to look at how much of each policy would be earned during the forthcoming year. But you're quite right, the data we're given would seem to imply a huge drop off in the amount of business written, so that can't be right.

Instead, let's think about the number of policies in force at the start of the year and the end of the year.

Number in force at the start = 288280
Number in force at the end = existing policies + new policies - cancellations =288280 + 19000 + 9000

So the average number of polices in force during the year is the average of these figures, which is
288280 +19000/2 + 9000/2
 
Thanks Katherine.

I figured this was the approach that should have been taken.

Just a bit confusing with what the terminology used is actually telling you. I guess it's cases like this where common sense needs to take over! :)
 
Katherine Young said:
Number in force at the start = 288280
Number in force at the end = existing policies + new policies - cancellations =288280 + 19000 + 9000

So the average number of polices in force during the year is the average of these figures, which is
288280 +19000/2 + 9000/2
Click to expand...
Hi Katherine,

If the 288280 policies were in force at the start of the year, wouldn't they be expired by the end of the year?
 
That's exactly the trap that PDF1987 fell into Aditya.

You're interpreting the question to mean that none of those 288280 polices renew. This would give a catastrophic fall in the number of policies in force over the year, as PDF quite rightly said.

We have to think that can't be right, and interpret it as per the explanation below.
 
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