S/U ART question: q[x+5]+t-5 = qx+t?

[dekenstr]

In the middle of the page 552 of Select and Ultimate renewalble term note, it says:

Fifth, for t >=5 + (pricing mortality select period) ... q[x+5]+t-5 = qx+t

It seems simple but I am afraid that I cannot understand it. My view is that q[x+5]+t-5 is the mortality of a newly underwritten life, it shall be lower than the ultimate mortality of the same attained age (x+t), i.e. q[x+5]+t-5 < qx+t

Can anyone help me out of this low-level question?

Thanks in advance.

[OceanFar]

I think this is what it meant:

q[x+5]+t-5 = qx+t will be true at the end of the new select period for the newly underwritten, i.e. t >=5 + (pricing mortality select period).

So if the pricing mortality select period is 15, and a reverter qualifies for select rates at time 5.
q[x+5]+t-5 < qx+t for 5<t<20
q[x+5]+t-5 = qx+t for t>=20

[dekenstr]

Thanks for reply.

I think you actually have the same view as me: the equality is only valid when t is beyond the select period as the reverters start over selection again. In your example, for 5<t<20, the equality is not valid.

But the note says "for t >=5+" instead of saying "for t>=5+select period"...

That really confuses me.

[dekenstr]

"This method uses the concept of conservation
of total deaths. The excess lapsers are
assumed to be fully select at the time of
lapse, but their mortality grades to ultimate
in normal fashion."

-- this is taken from pdn0307 "Mortality Anti-selection — Different Versions of Dukes/MacDonald by Douglas C. Doll"

OK. I think I finally understand it although I still feel the assumption fishy.

[Mel]

IIRC, the select period in that example from the S/U ART article is 5years. I think it was a bad choice since the time of reversion was also 5years. Perhaps this is where the confusion is coming from.

[Gandalf]

Thanks for reply.

I think you actually have the same view as me: the equality is only valid when t is beyond the select period as the reverters start over selection again. In your example, for 5<t<20, the equality is not valid.

But the note says "for t >=5+" instead of saying "for t>=5+select period"...

That really confuses me.
I don't have the original source, but what you wrote in post 1 was for t >=5 + (pricing mortality select period), which is the same as "for t>=5+select period". What would "for t >= 5+" mean anyway? "t>=5" makes sense, as does "t>5" but not "t >= 5+"

[dekenstr]

I don't have the original source, but what you wrote in post 1 was , which is the same as "for t>=5+select period". What would "for t >= 5+" mean anyway? "t>=5" makes sense, as does "t>5" but not "t >= 5+"

Sorry I was buried up at work and haven't visited the site for a couple of days.

I think you are right. I guess that I mis-interpreted the bracket as a note instead of maths...

I will take a look again.

[slystarnes]

Do you feel the discussion of this paper is considered fair game? The first discussion of the paper seems like another paper in and of itself.