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#1




(1+q)^(1/12) 1 vs. 1(1q)^(1/12)
Hello! I've been looking around and seem to not be able to find an answer. Can anyone tell me if they have ever seen [(1+q)^(1/12)]1 used in place of 1[(1q)^(1/12)]? The q can be death, exiting a policy (in terms of disability, etc). I am not looking for i or d in this case, even though they are similar.
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ILALPM ILALFM DMAC FAC Last edited by koudai8; 07112017 at 06:02 PM.. 
#2




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#3




"[(1+q)^(1/12)]"
Where did you see this? And what sort of probability theory do you think would support a plus sign??
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#4




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I'd expect to see something like 1Px=1/(1q), where q is a rate of observed decrements with the prior year as the exposure base and where the 1Px gives you the relative size of an inferred past population relative to a known one, but someone, somewhere might have invented a reason to study the q in the backward direction. That's the only rationale I can come up with. 
#5




OK, I guess. Somehow I doubt that's what the OP had in mind. But if it was, then the formula to use simply depends on the convention you use for q. Right?
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Carol Marler, "Just My Opinion" Pluto is no longer a planet and I am no longer an actuary. Please take my opinions as nonactuarial. My latest favorite quotes, updated Nov. 20, 2018. Spoiler: 
#6




I saw something like this for UL COI charges years ago, but darned if I remember the explanation for it; I also seem to recall seeing this discussed elsewhere on the AO.
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#7




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I do hope the person who posed this problem will come back and explain how the formula is intended to be used. ETA  I wonder how similar the two formulas would be if you took just the first few terms of a Taylor expansion. I leave this as an exercise for the student.
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Carol Marler, "Just My Opinion" Pluto is no longer a planet and I am no longer an actuary. Please take my opinions as nonactuarial. My latest favorite quotes, updated Nov. 20, 2018. Spoiler: 
#8




Thank you much for replying. TBH Im an intern (my first internship) and my manager just asked me to do research and see if I've seen this formula used, but not using i or d. So just seeing it anywhere and using q as either exit rate, mortality rate, etc. Basically, leaving a plan. I'm assuming it relating to pricing or modeling a life or disability plan.
*This isn't my account. One of the other inters let me borrow it. So I actually only have 2 exams passed.
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#9




Assuming the q is a decrement (which they usually are), the reason I don't think the "plus" version could ever work is because, it doesn't get you to the right place after 12 months.
Take a decrement of 1% as an example. Turning it into a monthly decrement using the "minus" version gives you .000837. If you start with a population of 100,000 and apply that decrement each month you end up with 99,000 left after 12 months. As you would expect you lost exactly 1% over the course of the year. Using the "plus" version gives you are monthly value of .00083. Again starting with a population of 100,000 and applying the "plus" decrement each month for 12 months, you end up with 99,009. I think this is as simply as the "plus" version should be used for accumulating (like interest) and the "minus" version for decrementing.
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#10




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Using a 1/12 per month uniform or a ^(1/12) multiplicative factor are both reasonable and have their place, but you could "disprove" either of them with this kind of logic. Using 1+q is an unusual choice, as the force increases through the year, but I could imagine using it in the scope of a larger problem if it simplified the math. 
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