Select Mortality

[Scotty]

Hi,

Can someone please tell me when you know that the select mortality no longer applies in a situation. For example, Q&A bank 1, question 1.11 (i), it uses select mortality for the first two years and then uses ultimate (in the solutions). Any ideas?

Also part (ii) doesn't use select mortality for the numerator in the second expression of the formula (also given in the solutions).

Kind regards,

Scott

 

[Calum]

On the face of it, that doesn't sound right, unless the question has told you specifically. Select mortality applies at the specific time since selection.

 

[Scotty]

Found the answer. In the 'non-core' reading it says that AM92 is select for two years. It should state this in the core reading.

Thanks

Scott

 

[bystander]

Is AM92 in the actuarial tables? If so, that should make it clear too.

Don't think construction of tables is in the syllabus hence its not core.

 

[PPActuarial]

With respect to Q&A part 1 / Question 1.11 (ii), I had exactly the same questions but do still understand only partially:

I do understand that after the the select period there is no difference in mortality rates or survival probabilities for the select or the ultimate case. However, with respect to the number of survivor for a particular age x (denoted by a small L in the tables), I would understand that later L's also beyond the select period would still be different from ultimate L's. In this particular question, I would hence have expected that not only the l[40] is select, but also l[50] instead of l50. Why is this not the case? (The same issue can similarly be found in question 1.22: Why is it l62 rather than l[62]?)

Many thanks in advance for sharing your insights!

 

[Calum]

The thing to remember about l_x is that it really is just a proxy to the distribution function, and persists partly for historical reasons and partly because it is such a natural interpretation of the distribution of survivors.

So, yes, if you took 100,000 newly underwritten lives with a select period of 2 years, and 100,000 non-underwritten lives from the same population, after (say) five years, you will have different numbers of lives.

However! If you then take the number of lives in year six, you will find the ratio between years five and six is the same for both (in theory - in fact the select effect lasts much longer than is actually typically shown in tables).