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JamaicanJem JamaicanJem is offline
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Default Exposed to risk interval defns. - 10-03-2008, 01:35 AM

Hi guys, as u can see, I'm a little behind with CT4 but neways I have a ques. about the exposed to risk defn for calendar rate intervals...
On page 24, it states that P(x+1, 1 Jan next year) is the same as P(x, 31 Dec).
Can anyone explain this because I think that by 1 Jan next year, the number of ppl in the group would have changed because of Dx, etc....


Thanks.
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JamaicanJem JamaicanJem is offline
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Default 12-03-2008, 05:47 PM

Any help here....
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Robert Chadburn Robert Chadburn is offline
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Default 12-03-2008, 07:27 PM

Hi - here goes.
It is saying that the people with age label x at 31 December are the same people who have age label x+1 one day later (1 Jan). This is because the age label x is age x next birthday on previous 1 January. So at 31 December, someone with age label x is aged x next birthday at previous 1 January - which is a year ago - so in 1 day's time they will all be x+1 next birthday.
Now try reading the above again slowly while sober...
Makes sense or not???
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JamaicanJem JamaicanJem is offline
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Default 12-03-2008, 08:45 PM

Hmm, Thanks Mr. Chadburn...
(BTW I'm always sober)....

But I guess the real issue is the fact that the equation represents the time from the beginning to the END of the interval which would be Dec. So everyone would be x+1 by Dec 31, which is fine by me... but how come this doesn't apply to the rest of the intervals like the life year interval... why is the calendar one different since by the end of any interval, everyone would be x+1 anyways.... Catch my drift?

But thanks though.
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Actuary Actuary is offline
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Default 13-03-2008, 12:11 AM

Calendar year rate interval is slightly different to life year or policy year rate intervals. Lives defined as age x in a calendar year rate interval all become age x+1 at the same time. Wheras for life year interval, lives each become age x+1 on their respective birthdays, or policy anniversaries for policy year rate intervals.

To pick up on your point "So everyone would be x+1 by Dec 31"; this is misleading since all policyholders only become x+1 at midnight on dec 31; As this is when the age definition switches. Can say 1st jan and 31st dec are approx the same because not many policyholders are expected to die in the one day.

Why does P(x,31 dec) not equal P(x+1, 1 jan) for life year interval? Because the age x do not move to x+1 at the end of the year, but on their birthdays. So most x's will stay age x, unless their birthday is 1 jan.
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JamaicanJem JamaicanJem is offline
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Default 13-03-2008, 04:48 PM

Ohhh... well I think I have a better understanding... but I guess I didn't want to make the assumption that approximately noone will die between dec 31 and jan 1. Thanks alot.
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