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Long-Term Actuarial Math Old Exam MLC Forum

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  #1  
Old 06-13-2009, 04:21 PM
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Default Another question: ASM Problem 14.3

Given that and for end of year insurance (EOYI), in the solution we have

.

For EOYI the pure endowment is given by

This is correct isn't it?


Now for EOYI, is it true in general that the pure endowment is given by .


I cannot figure out how ? Can anyone help me with this? Am I missing something? Thanks!
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Old 06-13-2009, 06:20 PM
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Originally Posted by (/iropracy View Post
Now for EOYI, is it true in general that the pure endowment is given by .
Yes. A (unit) pure endowment pays $1 at the end of the period if (and only if) you're alive at that time. So , i.e. the product of the probability that you survive to receive the payment times the present value of that payment.

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I cannot figure out how ? Can anyone help me with this? Am I missing something? Thanks!
They're not equal. is the value of a policy that pays $1 at the end of n years if you died sometime over the course of those n years** (note: I had to change the upper limit of the sum to n-1 for what I just said to be correct) -- it's sort of the logical opposite of a pure endowment, which pays if you've survived those n years.

** This is easier to understand if you first rewrite the sum as
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Old 06-13-2009, 11:55 PM
Abraham Weishaus Abraham Weishaus is offline
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No equality of this type appears in the question or solution to ASM 14.3.
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Old 06-15-2009, 02:04 PM
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Ok your right that the equality is not given anywhere in 14.3.... but the implication (so I thought) was.

So to change the question ..... is the following correct for an end of year pure endowment..



In the continuous case we sum with but on eoy we don't... is that correct?
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Old 06-15-2009, 02:14 PM
Abraham Weishaus Abraham Weishaus is offline
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As Jeff Raven said, no. You're thinking of a term insurance, not a pure endowment, and the range of indices isn't right.
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Old 06-15-2009, 02:17 PM
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That's what I thought. Yep, still learning.
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