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Old 01-12-2019, 09:21 AM
ingenting ingenting is offline
Non-Actuary
 
Join Date: Jan 2014
College: University of Washington
Posts: 20
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Quote:
Originally Posted by Gandalf View Post
I didn't follow all the steps, but ∫ v^t*fx(t) dt depends on mortality and
e^(-δt) - ∫-δ*e^(-δt)dt does not depend on mortality so something must be wrong there.
The mortality vanishes after integration by parts. I set
u = e^(-δt) v= 1
du=-δ*e^(-δt)dt dv=fx(t) dt
I set dv = fx(t) dt and when you go back from dv to v, you integrate dv from 0 to infinite to get 1. The formula for integration by parts is:
u*v - ∫v du
there is no mortality anywhere in equation, that's how the mortality just disappears. I agree that things get a little weird here but I couldn't find out what goes wrong.
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