# Multiple state question - Test 2 2020 3(c)

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Hi

Could you please explain why it is necessary to calculate A^HSD in this question? What does A^HD represent? (I'm assuming it's an assurance paid upon the death policyholder who was healthy at inception of the policy)

In that sense, doesn't A^HD already include the probability of dying from the critically ill state since the life was healthy at the inception of the policy, and they will be paid so long as they are healthy at inception and dead at time t?

Thanks

by (2.9k points)
You are quite right. Normally, the HD would incorporate both paths. In this question, they are trying to illustrate the transition from H->D only (because you need to break each path up so you can work out the answer). This is not very clear labelling and in order to understand what they are doing, you need to look at the workings of their expression to see that they are only referring to the single case from H->D without going through S.

I am not sure there is a clearer way to label this expression so, in the future, look out for what they mean when they say HD and be clear yourself (often they will ask you to explicitly state what you mean in the start of the question and even if they don't, do it anyway so that your answers are not misunderstood and it's clear what you mean...if that means being better than the way the memo wrote it, then do so an be proud at how much clearer your answers are to them!)

A side note, it's important to understand that the memo's are not written as notes for students to learn.  They are written to help markers mark. This distinction is important to understand as you can write answers better than the memo. Don't think that the memo is the gold standard or necessarily the best answer, but it is an answer which often holds a lot of merit and understanding where and why it has merit (and where it could be better) is part of the learning process so it's very good that you are asking these kinds of questions!
by (1.1k points)
edited by

Thanks, so in this case they didn't explicitly state what A^HD that was given in the question means/includes, what is the default definition that we should assume in a situation like this by just looking at the question? That it includes the transition directly from H to D only?

by (2.9k points)
In terms of your answer, make sure you define it and don't leave it up to chance. It all depends on how you use it.

In terms of understanding a memo, keep reading and work it out for yourself. Here, they showed you how they defined it through the workings. There isn't a "default" definition that I know of. Some people read it differently which is why you can't leave your answers up to the interpretation of the marker (much like when you work one day, you can't leave your answers up to the interpretation of anyone who sees it).

It's a non-answer but that is the best one I can give you because I've seen it used for both H->D with all the paths and H->D as a single path. Here it was made clearer by the way they defined the first line of the question and then simplified to it this.

Again, the memo isn't always perfect so developing your own answering technique is the important thing to take from this.
by (1.1k points)
Oh okay, I fully understand the memo and have no problems with it, just with the actual test question itself. I'm asking because they gave A^HD = 3636.36 in the question information so I did not calculate A^HSD and just used the 3636.36 as is because I thought A^HD already includes it as per intuition and they did not say anything in the question that would make me think otherwise. If I stated in my workings that I assumed the A^HD = 3636.36 includes A^HSD I would have still gotten the answer wrong as per the memo so I was just curious as to what I should do in a similar situation in the exam, when the question does not define the notation. Thanks
by (2.9k points)

In this case, the question totally 4 marks when they gave you everything you needed wouldn't make sense. It was the mark allocation that indicated what they meant.

In the exam, when these questions are vetted a number of times, it will be clear what they mean.

For me, when I see assurance/annuity functions of HS or HD, I always assume that's the direct route and not inclusive of every path. I think it's only for the P functions (i.e. mortality functions) that the HD incorporates all the movements between states between Hand S or H and D. I think this is something you can use (whilst also keeping in mind the mark allocation) that will help you know which thing they mean in each situation.
by (1.1k points)
Thanks for the help!