Hi, I’m struggling understanding some of the multiple decrements questions and hoped for your help. April 2016 Qu9 I understand the solution when I read it, however my first approach was to calculate the following: 250000*v^0.5*1p^HH 63*0.03 + 325000*v^1.5*2p^HH 63*0.03. When I have attempted similar questions such as April 2018 Qu9 this has worked and is the solution. Could you please highlight where I have gone wrong here? I think my problem is understanding the difference between tp^HH x and t(aq)x^d. Is there is an obvious hint in the question when to use tp^HHx or t(aq)x? Thanks
Hi sfollowedbysomenumbers It looks to me as if you've tried to write this in the same sort of way as you would do an integral, but you don't actually have an integral and an integral approach would require a factor of v^t rather than v^0.5. We use the (aq) notation when we're dealing with a multiple decrement model and we use the tpx^HH notation when we're dealing with a multiple state model. We have a multiple decrement model when we're only interested in the first transition that occurs, ie the change out of the initial (active/healthy) state. That's appropriate in April 16 Q9, as the only time any benefit could be paid is if the first transition is from active to disabled. When we calculate an EPV, we consider: amount of payment * discount factor * probability/PDF of payment in that year and sum/integrate over all possible years of payment. If a question tells us that forces of transition are constant or gives us a formula for forces/probabilities, it's usually straightforward to do the integration. Otherwise, it's acceptable to use the halfway through the year approx for the payment time. If you're using the halfway through the year thing, you need to make sure that your probability involves an (aq) factor. You can't use a probability multiplied by a force of transition when doing this kind of approx (as you have in your expression above). If we are interested in transitions after the first one, ie if the diagram has arrows from states other than active/healthy, then it's a multiple state model. This is appropriate if we're thinking about benefits payable on transition from sick to dead, or benefits that stop when a life recovers. Hope this helps Julie
