MII (A + da = 1)

[Brutè]

Most Important Identity, as Batten calls it. From Chap 5.

A + da = 1

Does this not work for n-year, fully discrete term?

For example, if we're given q's and i on a three year term we can figure out Ax by using v q0 + v^2 p0 q1 + .....

But can we use the resulting Ax and the MII to figure ax or do you have to find ax the long way too? (1 + vp0 + ...)

[E]

The insurance factor must either be a WL insurance or an endowment to use the "most important identity" to calculate the corresponding annuity factor. If you know the term insurance factor, simply add on a pure endowment factor and then use the MII.

[Sunny]

Originally Posted by E

The insurance factor must either be a WL insurance or an endowment to use the "most important identity" to calculate the corresponding annuity factor. If you know the term insurance factor, simply add on a pure endowment factor and then use the MII.

hmm.. really....

I would have intuitively guessed that it's true for WL and pure endowment, but not endownment or term....

[funk1]

Just remember, in Batten speak, the "two twin benefits." That is, you can go directly from endowment ins to def ann and from whole life to whole life. No other way about it if you do it in one step (yes, adding the pure end is req to ultimately get to term ins). This is true for the variance of the annuity random variable as well where you have the variance for the insurance in the numerator and d or delta in the denominator.
In your mind, you should try to connect all that together and that will keep you from making illegal assumptions on exam questions involved with this.

[Sunny]

Again, question here, do you mean from WL to WL annuity and term benefit to term annuity? I'm lost!

[Jim Daniel]

The relation "a = (1 - A) / r"
holds:
1) with "a" meaning "a-double-dot" and "A" meaning "A" and "r" meaning the discount rate "d"
and
2) with "a" meaning "a-bar" and "A" meaning "A-bar" and "r" meaning "delta".

In both cases, EITHER put a status like "40" or "x" or "x:y" or "xy-last-survivor" as subcripts on _both_ "a" and "A", OR put one of those statuses with an "angle-n" added on as subscripts on _both_ "a" and "A".

Jim Daniel

[Sunny]

Thank you!