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CT5- CH8 Last Survivor Reserve

S

Sunil Sanga

Member
Please help me to understand how reserve be largest in case of male survivor in this question?

Question:
For a policy where the male and female are both aged 63, list the 3 possible states that a
last survivor assurance may be in after a few years. For which of these would the
reserve be largest?


Answer :
The 3 possible states are:
 both lives still alive
 male life still alive
 female life still alive.
We would expect that the sum assured be paid out earliest on the policy where just the
male is still alive. This policy would therefore most have the largest reserve.
 
Question is from.. CMP, QnA or past exam?
Please mention q no. Or page no.
 
Hi Deepak,

This is question 8.10 on page 17 in ch8
 
I think its generic answer.
Generally the female mortality is lesser than the male. On an average there is difference of 4 to 5 years, means male dies 4 to 5 years before female. In our case both are of 63. So P( male dying ) is always higher and if in this case male survives then naturally required reserve is largest.
This is my view. Not sure how much is correct?
 
Deepak is correct, and it essentially comes down to the fact that on average women live longer than men.

Ignoring expenses and premiums (imagine there was just a single premium at the start so you don't need to consider the EPV of future premiums), you can think of the prospective reserve as the present value of the amount of money that you expect to pay out for benefits in the future. The longer it takes for both lives to die, the lower this present value will be. If you need to pay out the benefit in 5 years, it will be discounted by 5 years of interest, but if you need to pay out in 10 years, it will be discounted by 10 years of interest.

Suppose that on average a male lives to 75 and a female lives to 80 (just making these numbers up, all that's important is that females live longer than males on average), while both lives were alive you would have been expecting on average to have to pay out in 17 years time when the female dies. However, given that the female has already died, you're now expecting to have make a payment in just 12 years time on average. Therefore if the female dies, the expected present value of future benefits increases, so the value of the reserve increases.

The order of the size of the reserves for the 3 scenarios would be:

Both alive < only female alive < only male alive

And the reason that the reserve when both are alive is greater than when just the female is alive is because you are then taking into account the chance that the male ends up living longer than the female.

Hope that helps.
 
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