I didn't find a way to achieve what I wanted using SSAS. Instead, I created created a table (or view) with the data I needed for this cube:
I have 1 row for each day that the person was alive.
I used the same idea for dealing with similar problems: - Call Center: calls per day: calls that were open (at any point in time) per day. - Shipping: in-transit per day: orders that were in wait state in the warehouse and waiting to be shipped per day.