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  #1  
Old 09-08-2018, 01:36 AM
JohnTravolski JohnTravolski is offline
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Question Confusing Notation for Select Life Tables

The bracket notation for select life tables really confuses me, and I can't wrap my head around it. So I am going to present several statements below, listed as A through H, some of which may or may not be true. Please identify which statements are false and which are true, and under what circumstances they are true to help me understand, because I genuinely have no idea about any of them. The notation is just too confusing to me.

So for a select life table with three years select period that begins at age 0, which of each the following are true, and under what circumstances?



For reference, this is the same notation used in:

Dickson, D.C.M. and Hardy, M.R. and Waters, H.R. - Actuarial Mathematics for Life Contingent Risks, Second Edition (2013, Cambridge University Press)
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Old 09-08-2018, 09:51 AM
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Colymbosathon ecplecticos Colymbosathon ecplecticos is offline
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You have no idea about any of them? Then we can't help you at all.

Why don't you tell us what you think the right-hand side and the left-hand side of A) represent to get started?
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Old 09-08-2018, 11:52 AM
JohnTravolski JohnTravolski is offline
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Quote:
Originally Posted by Colymbosathon ecplecticos View Post
You have no idea about any of them? Then we can't help you at all.

Why don't you tell us what you think the right-hand side and the left-hand side of A) represent to get started?
I think l[x] is the expected number of survivors that were selected at age x, while lx is the expected number of survivors to age x.
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Old 09-08-2018, 12:08 PM
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The select l's are constructed from a table of select and ultimate q's. Constructing a select and ultimate table of l's requires a starting point which is the select l in the upper left hand corner. It is an arbitrary number, generally some power of 10.

You then have to complete the top row moving left to right using the q's, until you reach the ultimate column. You then fill in the right most column using ultimate q's. With this final column you then move row by row going right to left. The select and ultimate l's are simply values that will replicate the select and ultimate q's.
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Old 09-08-2018, 07:49 PM
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Quote:
Originally Posted by JohnTravolski View Post
I think l[x] is the expected number of survivors that were selected at age x, while lx is the expected number of survivors to age x.
What does that mean?

Make it simpler. Let's assume a 1-year select period. Also assume:

l(50) = 950
q(49) = 0.0500

What is l(49)?
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Old 09-08-2018, 08:02 PM
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When you've done that one:

Same set up. Now you are told that q[49] = 0.02

What is l[49]?

How are these two l-values different?
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Old 09-09-2018, 03:15 PM
JohnTravolski JohnTravolski is offline
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l(49) would be 1000, but I'm not sure how to calculate l[49].

Is it true that q[49] = 1 - l(50)/l[49]?

If so, why isn't it q[49] = 1 - l_{[49]+1}/l[49]?
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Old 09-09-2018, 03:35 PM
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It is, and since the select period is one year ...
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Old 09-09-2018, 05:41 PM
JohnTravolski JohnTravolski is offline
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Then l[49] is 969.3877551

Okay, I think that was my primary confusion with all of this. For some reason I wasn't making the connection with the duration of the select period.

So, essentially, I think it comes down to this:



This is my current understanding. If this is correct, please let me know. If I am incorrect or a detail needs to be changed, please inform me. Thank you.
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Old 09-15-2018, 11:44 AM
JohnTravolski JohnTravolski is offline
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Would somebody please confirm that the formula I provided above is correct? Thank you.
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