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Ch. 13 Multiple Decrements

N

nmellor

Member
Hi

I am just a bit confused by two points of the theory in Chapter 13:

- On page 8 it says the expected number of additional decrements from cause k in (x,x+1) is 1/2 * (ad)^-k * q^k. How is this obtained?

- On page 14 it says q^alpha = t_p^alpha * mu^alpha. Surely the inital rate of mortality is the sum of the RHS over all values of t from 0 to 1?

If you could help that would be appreciated.

Many thanks

Nick
 
Hi Nick,

Anyone who leaves due to decrement other than k does so, on average halfway through the year. Bring these people back and then apply a qk to them.

You're right on your second point but the LHS is already in an integral between t=0 and t = 1 above. The CR is saying we can take these two terms as a constant outside the integral because the decrements are uniformly distributed,

Good luck!
John
 
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