Conservation vs Preservation of Deaths

[LifeAct]

What is the difference between Conservation of Total Deaths and Perservation of Total Deaths? I thought that they were the same concept with different names in different sources. Fall 07 disagrees with me.

[Toluca]

Both used to calculate anti-selection.

Preservation of total deaths - Chapter 3 of LIPF book
Weighted average on the mortality rates


Conservation of deaths - Experience assumptions for ind life and ann study note
weighted average of total population will be equal to the aggregate mortality assumption (uses total deaths Lx times Qx)

Hope this helps

[LifeAct]

I like the explanation in LIPF for Preservation of total deaths. I can follow this with no problem. I guess that it is the Conservation of total deaths that I struggle with, the study note is not very good at describing the idea. I'm hoping that since it was asked last fall, they won't ask it again. I am going to keep going over the question that was asked last year and try to figure out an intuitive difference.

[Inigo Montoya]

As usual, inexactuary provides a good explanation in this thread: http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=115492
Basically, Conservation of Deaths assumes that 100% of lapses are selective while Prervation of Deaths assumes some number less than 100% are selective and the other lapses have normal mortality.

[inexactuary]

The silly thing about this question is that there is nothing special about using the word conservation versus preservation, so the names used by the authors could have just as easily been identical. They are really the same thing, but one author uses a slightly more complicated model than the other. That said, I'm sure you would have gotten full credit if you had the names switched.

[LauraJane]

Isn't one of these in the Pricing S/U ART study note which was removed from the syllabus? I thought I remembered Jeremy touching on that at the seminar that one of these 'methods' had been removed from the syllabus.

[inexactuary]

Isn't one of these in the Pricing S/U ART study note which was removed from the syllabus? I thought I remembered Jeremy touching on that at the seminar that one of these 'methods' had been removed from the syllabus.

If memory serves correctly, there were at least 3 sources that covered this topic, and the Pricing S/U ART study note was the odd man out in that it had a slightly different method (no idea whether it was "conservation" or "preservation"). So if that study note has been removed, then I think you are correct that there is only one method left on the syllabus.

[LifeAct]

If memory serves correctly, there were at least 3 sources that covered this topic, and the Pricing S/U ART study note was the odd man out in that it had a slightly different method (no idea whether it was "conservation" or "preservation"). So if that study note has been removed, then I think you are correct that there is only one method left on the syllabus.

Was that source removed after the '07 sitting? Last years exam asked candidates to calculate persister mortality using "conservation" and "preservation" methods.

[inexactuary]

Was that source removed after the '07 sitting? Last years exam asked candidates to calculate persister mortality using "conservation" and "preservation" methods.

It was definitely on the syllabus for '07.

[LauraJane]

Was that source removed after the '07 sitting? Last years exam asked candidates to calculate persister mortality using "conservation" and "preservation" methods.


It was removed for the 2008 syllabus. Definitely on the 2007 syllabus.

[rekrap]

Isn't "conservation of deaths" still a term used in ILA-D107-07 which is on the syllabus?
How does that method compare to LIPF's "Preservation of Total Deaths"?

[LifeAct]

Isn't "conservation of deaths" still a term used in ILA-D107-07 which is on the syllabus?
How does that method compare to LIPF's "Preservation of Total Deaths"?

I believe that LIPf sets the original mortality as q*(1-w) where q = normal mortality and w = normal lapses. It also makes use of a select percentage, some of the extra lapses will still get the q(normal).

the D107 study note does not use either of these variables. They assume that all of the extra lapses are select.

[rekrap]

Here's my notes:
SN107
q(x,t) = mortality rate at dur t for policy issued at age x (no selective lapse)
A = portion of policies lapsing at duration r to buy new policy at x+r
qAS(x,t) = mortality rate at dur t reflecting effect of anti-selection

New policies + remainers = mortality with no selective lapsation
Aq(x+r,t-r) + (1-A)qAS(x,t) = q(x,t)
-> qAS(x,t) = [q(x,t) – Aq(x+r,t-r)]/(1-A)


LIPF Ch 3The probability of normally persisting (1 – qwnorm) is equal to the probability of actually persisting (1 – qwnorm – qwextra) plus the extra lapse probability (qwNon-Sel + qwSelect) which leads to:

(1 – qwNorm)* qdNorm =
(1 – qwNorm - qwExtra) * qdActual + qwNon-Sel * qdNorm + qwSelect * qdSel

Solving for qdActual:
[(1 – qwNorm – qwNon-Sel)* qdNorm – qwSel * qdSel]/ [1 – qwNorm – qwExtra]


I interpret this to imply that this question is still applicable, as the first assumes all lapses are selective, while LIPF has some allowance for Non-selective lapses.

[LifeAct]

I interpret this to imply that this question is still applicable, as the first assumes all lapses are selective, while LIPF has some allowance for Non-selective lapses.

That is the difference as far as I am concerned. If I get it wrong, so be it.

[rekrap]

That is the difference as far as I am concerned. If I get it wrong, so be it.

There's no way they'd ask it again, now that everyone should be expecting it, right? :tfh:

[Berners-Lee]

I will stick to the concepts (to the extents the formula and the presister/revertor, etc) but I would not go into details with it.