CT5 September 2009 Question 11 (Booklet 10 - Question 4)

[Petros Kyriacou]

Hi,

Could anyone help me understand the solutions to the following question? I do not fully understand why the EDS and ADS have been calculated in the following manner.

Thanks in advance

 

[Bev.Butler]

Hi Petros
The EDS can be calculated in the same way as in any other mortality profit question. The reserve at the end of the year in question (ie age 61) is the EPV of future benefits less premiums. Here they have calculated benefits as an endowment assurance plus a pure endowment (getting twice as much on survival means this is the best approach). Then the EDS is the probability of dying in 2008 (q60) multiplied by the DSAR ( DSAR=payment on death - reserve).
We normally calculate the ADS by multiplying the DSAR by the actual number of deaths. Here we don't know the actual number so we use a different approach. The actual death strain is the additional cashflow on top of the reserve resulting from the deaths that have happened. If the deaths hadn't happened the reserve would be EPV future (bens - prems) using the sum assured and premiums given. But 100,000 had to be paid out so the additional cashflow (ie the ADS) is 100,000 - 141,480.
Bev

 

[Petros Kyriacou]

Hi Bev,

Thank you for your response. You've cleared up my lack of understanding for this particular question. I have one other question which relates to the recursive relationship for reserves. When asked to calculate the total profit or the interest profit we are often expected/asked to use the recursive relationship to do so. The solutions however seem to calculate it in a different way, to the formula which I have highlighted. The attached images relate to question 11 part (iv) and 12 part (iii) of booklet 10 (April 2013, question 13 and September 2013, Question 22 respectively) . It also seems to be a lot of work for something that is often only worth 2 marks, are there any shortcuts I may be missing out? For the record I have directly copied the solutions from the booklets.

Thanks,
Petros

 

[Bev.Butler]

Hi again
I am glad the first answer helped. In Q11 we are using the idea of the recursive formula that you wrote down (well a version where we do left hand side minus right hand side). The reserve at time 0 is 0 then premiums and expenses are as explained. The difference comes on the right hand side of the equation because we know what has happened so we don't use probabilities.
In Q12 it is exactly the same issue. The left hand side matches exactly then the right hand side again ignores probabilities because we know exactly what happened during the year.
Bev

 

[Petros Kyriacou]

Hi Bev,

I see. Thank you for this