TIA’s Exam MLC Blog

In lesson B.1.4 on page 6, I wrote

future lifetime is uniformly distributed b/w x and w

I should have said

future lifetime is uniformly distributed b/w 0 and w-x

Updates

I received this excellent question today:

Your solution for #51. Here you wrote e_[85] in terms of e_[87] first, then wrote e_[86] in terms of e_[87] and solved for e_[86]. Why does it not work to just write e_[86] in terms of e_[85] in one step?

My response:

We cannot write e_[85] in terms of e_[86], because [85] means a life selected (i.e. went through underwriting) at age 85. So we must write that in terms of [85]+1 which is a life selected at 85 one year later (as opposed to [86] which is a life selected at age 86). Does that make sense?

Follow-up:

So you’re saying you can write [85] in terms of 86 (and 87), and also write [86] in terms of 87, but not [85] in terms of [86]? That kind of makes sense.

My follow-up to his follow-up:

Yes, since this is a one-year select and ultimate table.

For our problem we have a one-year select and ultimate table:
For a life selected at 85 we have: [85], 86, 87, …
For a life selected at 86 we have: [86], 87, 88, …

The lowest common denominator is 87, so we write both in terms of that.

If we had a three-year select and ultimate table:
For a life selected at 85 we have: [85], [85]+1, [85]+2, 88, 89, 90, …
For a life selected at 86 we have: [86], [86]+1, [86]+2, 89, 90, 91, …

The lowest common denominator is 89.

Student Questions

I’ve added some solutions to the end of problems sets.  They can be found directly below the problem sets themselves on the main site only (see here).  These are problems that students have had trouble with and asked for solutions.  I’ll update these from time to time.  After I finish recording all the lessons and create a sample exam, then I will go back and add more solutions.

Updates

In the lesson I accidentally said the n-year temporary annuity twin is an n-year pure endowment, but I correctly wrote the symbol for an n-year endowment insurance.  The twin for an n-year temporary annuity is n-year endowment insurance.  Sorry for the confusion.

Updates

Many students have asked where to get this table.  Here is the link:

http://www.soa.org/files/pdf/edu-catfall07-exam-mlc-tables.pdf

Student Questions

I received the following question about the force of interest.

Regarding f(t), it seems like the difference of l(x) and l(x+1) would inherently include the force of mortality. So when you take nPx and then hit it with the force of mortality, it’s like the force of mortality is being implemented twice.

My response

The force of mortality measures the impact for one instant. nPx measures the impact between ages x and x+n. So if you want the probability of death exactly in exactly t years (which f(t) is), then you must live for t years then die at that very instant => tPx * mu(x+t).

Student Questions