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Use of Initial Exposed to Risk in the Binomial Model

D

density

Member
I'm confused by the the use of the initial exposed to risk in the binomial model.

As I understand it, the use of initial exposed to risk is justified Balducci assumption. Where can I go to see this justification explained? I assume that it has something to do with generalisation of the naive binomial model.

I also feel like central exposed to risk is poorly explained in the 2015 CT4 notes. Can anyone point me to a good explanation of how central exposed to risk is defined? An example of the sort of question I have is, why are the words "central" and "inital" used?
 
In the naive binomial model, we have D ~ Bin (n,q)
but this assumes everyone is observed from x to x+1
In fact, some lives join at age x+a and leave at age x+b
So, we then need to express the non-annual q in terms of the annual q. We have 3 choices:
UDD assumption
CFM assumption
Balducci assumption - we use this one because it makes all the maths work out nicely and the final answer is D~N(Ex,q)

Central Exposed to Risk is the total time actually spent observing everyone.

Good luck!
John
 
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