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
