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-   -   Fractional Age Assumptions (http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=120300)

 ndaka26 10-09-2007 09:01 AM

Fractional Age Assumptions

How do we deal with a fractional age assumption question (udd, constant, hyperbolic) when s+t > 1? Plugging the values into given formulas does not work.

 Abraham Weishaus 10-09-2007 09:05 AM

Take care of the integral part, then use the fractional age assumption for the fractional part.

For example, express as

or express as

 ndaka26 10-09-2007 09:27 AM

Quote:
 Originally Posted by Abraham Weishaus (Post 2373690) Take care of the integral part, then use the fractional age assumption for the fractional part. For example, express as or express as
Thanks Professor for the response. But I still don't get why we use survival propabilities when we are trying to find the probability of death/failure the expression 2.2qx = 2Px * 0.2qx+2 implies that 2.2qx = 2/2.2qx?

 Gandalf 10-09-2007 09:50 AM

He was just giving you the formula for the final fractional piece. E.g., the complete expression for the second would be = +

 Jim Daniel 10-09-2007 01:14 PM

Once a probability takes you outside a single integer year of age, it's often simplest to find the equivalent set of lx values from your year-long probabilities, express your complicated probability in terms of lx values, and then interpolate as needed (linear on lx, on 1/lx, or on ln(lx)) to get those lx values.

Jim Daniel

 ndaka26 10-09-2007 01:54 PM

Quote:
 Originally Posted by Gandalf (Post 2373751) He was just giving you the formula for the final fractional piece. E.g., the complete expression for the second would be = +
Gandalf thanks, I get it

 ndaka26 10-09-2007 02:04 PM

Quote:
 Originally Posted by Gandalf (Post 2373751) He was just giving you the formula for the final fractional piece. E.g., the complete expression for the second would be = +
would that be the same as qx + px * 0.2qx+1, though?

 Gandalf 10-09-2007 02:31 PM

No, because is not the same as qx (and similarly for the term you changed to px).

 urbjhawk 01-15-2019 10:03 PM

Can anyone help me with what u_(x+t) would be if t>1? We have that u(x+t) = q_x/(1-t*q_x) for when t<1 under the UDD assumption, but I can't seem to find a solution for when t>1.

 Gandalf 01-15-2019 10:19 PM

If you stop and think about it, you're asking a rather silly question. Fractional age assumptions are for the pattern of mortality between integral ages. So they tell you how to get (for example) mu_50.2 from q50. They wouldn't tell you how to get mu_51.2 (that's 50+1.2) from q50, because that's not in the year starting with age 50.

You could say mu_(50+1.2)=mu_(51.2)=mu_(51+.2) and then evaluate it under udd by the formula you already gave as q_51/(1-.2*q_51).

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