Hi Murray, thanks for the reply!

I'm still a bit confused, what happens if t=44,5, then won't the inner integral run from 0 to -0,5?

In the lecture slides with an identical question (see attached), the 1 is subtracted from the maximum possible term (30) of the benefit payments in the outer integral with respect to t, in order to account for the fact that the life has to be sick for at least 1 year, so why is that not the case here?

I'm under the impression that the extra factor of 1P_20+t^SS x V arises after one simplifies the inner integral with bounds 1 to 45-t, similar to the example in the lectures?