Commutation columns based on 2001 CSO

[tdbenson]

Does anyone know if commutation columns have been calculated based on the new 2001 CSO mortality table? In particular, I am trying to find the complete expectation of life (e-circle-x) based on the new table. I thought maybe I could just calculate it, but I'm apparently doing something wrong. I think I can calculate the curtate (e-x), but I don't know how to convert it to e-circle-x. Maybe I'm not even calculating the curtate right, who knows......

Any help, thoughts or ideas would be appreciated!

[Dick the Bruiser]

Hmmm...

Commutation functions are not needed for this calculation, if you ever need some you will need to create them yourself.

ex=SUM(kPx) from k = 1 to end
eOx=ex + 1/2 => (add .50 to ex)

ex=Px + Px*Px+1 + Px*Px+1*Px+2 + ....

[tdbenson]

The equations that you suggest are the same ones that I tried to use with the 1980 CSO table. The problem is that I didn't come up with the same eOx that they did, that's why I thought I was doing something wrong.

[Spectrum]

Jake assumed people die 0.50 through the year on average with a uniform distribution which is probably close enough. At some ages, old, the rate of mortality may be changing so quickly from age to age you might want to model it with some continuous function to get 0.48 or some other fraction close to 0.50. It might make a difference for an annuity calc of life insurance sold to 90 year olds.

[tdbenson]

I got it to work out. Thanks for all of your help!!