Where can I find the C1 problems?
March 14th, 2011
Archive
Archive for the ‘Student Questions’ Category
C.1.29
April 26th, 2010
I get asked about this question a lot. Take the case where she works #3 third. Students don’t understand why you can’t just use the probability of her solving exactly three problems. Here is why …
Poisson is defined over the domain 0, 1, 2, 3, …. So anytime we are using probabilities from the poisson we need to remember this. Considering the case where she works #3 third. Then the question becomes given she works #3 third what is the probability she solves #3? We are modeling the rate at which she works problems using the poisson so we consider the entire domain.
0 problems worked: did she work #3? no
1 problem worked: did she work #3? no
2 problems worked: did she work #3? no
3 problems worked: did she work #3? yes
4 problems worked: did she work #3? yes
5 problems worked: did she work #3? yes
and so on
so we need to add up the probability of working 3, 4, 5, … or we can just take 1 minus the probability of working 0, 1, or 2 problems.
How to study for preliminary exams …
November 30th, 2009
A student on the AO asked about how to study for preliminary exams. Here is my response.
AO thread
July 14th, 2009
http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=170426
If you have questions then that thread is a great place to post them. I will try my best to answer any questions posted in that thread within a day or two.
Joint Life Expectation Shortcut
April 30th, 2009
I’ve received a handful of questions about the following shortcut:
Please note that this works ONLY if you have DML for both lives. So if one of the lives is DML and the other is MDML this shortcut will not work!
Reserve Creation Formula Question
April 16th, 2008
I received the following excellent question:
I have a quick question about reserve creation formula. Why the formulas don’t take account tPx (survival probability)? Shouldn’t the accumulated benefit and premium be divided by those who survived?
My response:
We are subtracting the expected death benefits each time which in essence account for survival since you can only either live or die. Think of the reserve creation formula as money going into the bank. Each year we get premiums from all the people still alive (at the BOY). We pay death benefits at the EOY so multiply that expected benefit by v to bring to BOY. That net amount is what the company puts into the bank to help pay for future death benefits. When you put money into the bank you don’t need to divide by tpx to accumulate the money. So if we want the reserve at time t we just accumulate all those deposits into the bank to time t.
B.1.6 #51 question
February 12th, 2008
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.
Illustrative Life Table
February 1st, 2008
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
Question about force of interest
February 1st, 2008
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).