October 2010, Qu.4 - Calculation of Profit Criteria

[Korach]

I quote:

"It should be assumed that the premiums are received at the start of each year, the profit cashflows arise at the end of each year, the survivorship factors are the probability of surviving from the start of the policy to the end of the year shown and
the figures given are per policy in-force at time zero."

If the figures given are per policy in-force at time zero, then they should already take account of the survivorship factors, shouldn't they?

For example, if you tell me that a premium of 100 at the beginning of year 3 is per policy in-force at time zero, I would assume that 100 is the product of:
a) Premium paid at beginning of year 3 per policy in-force at that point
b) Probability of a policy in-force at time zero still being in-force at the beginning of year 3.

Neither ActEd or the examiners' report mention this possible interpretation, which probably means that I am misunderstanding the text.

We are supposed to take the view that every part of a question is written for a reason, so can someone please explain to me what the examiners were thinking when they wrote "and
the figures given are per policy in-force at time zero" ?

Thanks in advance and best of luck to all students who are still reading!!

 

[Robert Chadburn]

Crumbs, I see what you mean.

I guess you've got to try and use clues and common sense with something that may seem contradictory. If your interpretation is true, then the premium would have to increase very oddly (and coincidentally) in order for its value multiplied by the survival factor to be the level amount of 100 each year - more likely the premium is level at 100 per year.

The second clue is that, if it meant what you say, I would have expected to see the word "expected" in the phrase you refer to - ie it would say "the figures given are expected amounts per policy in force at time zero".

So what is it trying to say and mean? All I can think is that the "figures" are amounts that relate to a single policy, rather than to a group of policies (say). So a sinlge policy issued at time zero will be subject to a regular premium of 100 each year, and will also be subject to the given survival probabilities.

Also, remember that in ST1 they are not going to be asking anything over-complex with regard to CT5 (or any other earlier subject) material. The numerical calculations in ST1 are all of a pragmatic type - indeed much more like the sort of thing you would get in real life than the strictly correct routines hammered out to us in CT5. I'm not saying we should be doing it wrongly or haphazardly, just that we should be flexible and able to cope with odd data and definitions that may be thrust upon us.

On the day you can always get round any apparent contradictoriness by stating your assumption. So if you really believe that the premiums already include a survival factor, then state that you are interpreting it this way and calculate accordingly. You shouldn't be penalised provide all your calculations follow through correctly.

In summary, take a sensible approach, avoid being too complicated (chances are they didn't intend this!), state your assumptions, and you will be fine.

Good luck!

 

[Korach]

Thank you!