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Old 04-23-2018, 03:36 PM
ActuaryFromMTL ActuaryFromMTL is offline
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Default CA practice WA #2 question 3

Hi all,

If someone has a subscription to CA, how come the solution for the solution for exercise 3 b) doesn't take into account the benefit from going from state 0 to states 1, 2 ? Which are 1,000 and 10,000.

If I look at their formula sheet page 4, there is a b^(ij) that I don't see in their solution.

Thanks.
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Old 04-23-2018, 03:57 PM
Adapt and Chill Adapt and Chill is offline
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The solution for 3(b) does account for the benefit of transitioning into state 2.

When finding the time 7.9 reserve for V(0), the state 2 benefit is included in the term -(.015)(10000-1200). This is the force of mortality for 0->2 multiplied by the state 2 benefit minus the release of reserves for state 0.

When finding the 7.9 reserve for V(1), the state 2 benefit is included in the term -(.02)(10000-3100). This is the force of mortality for 1->2 multiplied by the state 2 benefit minus the release of reserves for state 1.


The state 1 benefit is paid continuously, so it's the -1000 in the V(1) solution. Because it's not a lump sum paid instantaneously upon transition, you don't include it in the same place as the death benefit---you should place it where you would put premiums/expenses.

Last edited by Adapt and Chill; 04-23-2018 at 04:06 PM..
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Old 04-23-2018, 04:40 PM
ActuaryFromMTL ActuaryFromMTL is offline
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Thanks Adapt and Chill. You are right.

Here is the mistake I made.

I thought the 10,000 in font of 0.015 for V(0) was actually the reserve at state 2 but THAT is the b^(ij) I was looking for. The reserve in state 2 is 0 because the benefit is already paid at that point
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