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Long-Term Actuarial Math Old Exam MLC Forum

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Old 03-13-2014, 05:41 PM
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Default ASM 12 Ed: Q65.7

Hi all,

I have a couple of questions concerning a Universal Life Policy problem. Here's what it asks in the manual:

Quote:
For a universal life policy on (40) with death benefit of $100,000 plus the account value:

(i) Expense charges of 6% of premium plus 100.
(ii) Cost of insurance is based on 120% of mortality using mu(x)=0.005*1.01^x, with benefits paid at the middle of the year.
(iii) Interest credited is 4.5% every year.
(iv) The policyholder paid premiums of 100 at time 8 and 500 at time 9.
(v) The account value at time 10 is 12,000.

Determine the account value at time 8.
I understand how to tackle this problem, but I have an issue in reading assumption (ii). First, when they say "120% of mortality," the solution used 120% of qx, not 120% of mu. I had originally thought it was the other way around.

Secondly, because benefits are paid middle of year, shouldn't the tqx probabilities be 1-year qx's from the mid-year? (For instance, q8.5 and q9.5) The solution just uses q8 and q9, but this seems silly to me. How can we pay out an insurance benefit at t=9.5 for a death that hasn't happened yet, but will occur within the next half a year? I thought it made more sense to pay out at t=9.5 for all deaths occurring from t=(8.5,9.5].

I guess what I'm asking isn't really mathematical or anything like that, but is this the way they'll be phrasing questions on MLC? I'd like to make sure I know how to read these types of things before the exam this April.

Thanks in advance!
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Old 03-13-2014, 11:12 PM
Abraham Weishaus Abraham Weishaus is offline
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Your first issue has some merit. I will try to improve the wording.
Your second issue, though, has little merit. We assume account values are updated annually unless told otherwise. Thus COI would be updated at birthdays. It would be unusual to use a COI for two different ages (e.g. 7.5 and 8.5 to update from year 8 to year 9) for the same year. The COI for the ninth year is based on the probability of death in the 9th year. Of course the payment isn't really made midyear, but this assumption is a convenient approximation for payment at the moment of death.
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Old 03-14-2014, 11:10 AM
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Phileas Fogg Phileas Fogg is offline
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"benefits paid at the middle of the year" does lend itself to the amusing interpretation above, but yeah, in the context of the problem I don't see it as inferior to

"benefits paid immediately, but assumed to all be paid at the middle of the year as a useful approximation and simplifying assumption"

which seems to be a little unwieldy.
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Old 03-14-2014, 10:28 PM
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Quote:
Originally Posted by Abraham Weishaus View Post
Your first issue has some merit. I will try to improve the wording.
Your second issue, though, has little merit. We assume account values are updated annually unless told otherwise. Thus COI would be updated at birthdays. It would be unusual to use a COI for two different ages (e.g. 7.5 and 8.5 to update from year 8 to year 9) for the same year. The COI for the ninth year is based on the probability of death in the 9th year. Of course the payment isn't really made midyear, but this assumption is a convenient approximation for payment at the moment of death.
Thanks, that clears things up. I was thinking of it as a contractual payment date - so that the "beginning" of the year occurs at a midpoint, and so does the end. If it's just a timing assumption for pricing purposes, it makes sense to calculate it the way that the solution says.
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