Actuarial Outpost (http://www.actuarialoutpost.com/actuarial_discussion_forum/index.php)
-   Group & Health Advanced Exam (http://www.actuarialoutpost.com/actuarial_discussion_forum/forumdisplay.php?f=191)
-   -   Fall 2019 FV-A #1 (c) (http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=347135)

 fightinphilz 03-15-2020 06:07 PM

Fall 2019 FV-A #1 (c)

I understand all the steps here in the SOA solution except for how they are calculating expected in-force contribution. Can someone explain how they are going from the formulas presented in the reading, to the formula they are listing there in the sample solution? namely, they say that

EC of IF business = [IBV (t-1) + RC (t-1)] x RDR

From the reading, the formula for line 5 of the AoM Report should be:
EC of IF business = IF EIBV (t) - IBV (t-1) = IBV(t-1) x RDR - IF BP(t) + CoC (t)

how do you get from the 2nd formula back to the first?

 Alemana19 03-25-2020 10:04 AM

Quote:
 Originally Posted by fightinphilz (Post 9827927) I understand all the steps here in the SOA solution except for how they are calculating expected in-force contribution. Can someone explain how they are going from the formulas presented in the reading, to the formula they are listing there in the sample solution? namely, they say that EC of IF business = [IBV (t-1) + RC (t-1)] x RDR From the reading, the formula for line 5 of the AoM Report should be: EC of IF business = IF EIBV (t) - IBV (t-1) = IBV(t-1) x RDR - IF BP(t) + CoC (t) how do you get from the 2nd formula back to the first?
I'll try to help when I get to doing problems for this objective. In the meantime, could you add in page numbers (formula in the reading) if you can? Or sections? I have both mate and the source materials so either/both work.

 MATEseminars.dc 03-27-2020 02:05 AM

EC help

Quote:
 Originally Posted by fightinphilz (Post 9827927) I understand all the steps here in the SOA solution except for how they are calculating expected in-force contribution. Can someone explain how they are going from the formulas presented in the reading, to the formula they are listing there in the sample solution? namely, they say that EC of IF business = [IBV (t-1) + RC (t-1)] x RDR From the reading, the formula for line 5 of the AoM Report should be: EC of IF business = IF EIBV (t) - IBV (t-1) = IBV(t-1) x RDR - IF BP(t) + CoC (t) how do you get from the 2nd formula back to the first?
Hello,

Your second formula is set up right but it is not equal to "EC of IF business" as you have stated. It is equal to "the in-force business expected increase in IBV"

So it should be (see page 22 of source formula #18):
the in-force business expected increase in IBV = IF EIBV (t) - IBV (t-1) = IBV(t-1) x RDR - IF BP(t) + CoC (t)

Then to get from there to the EC of IF business ....

EC of IF business = expected increase in IBV plus expected net income (page 22 of the source material)

Using your formula: expected increase in IBV = IBV(t-1) x RDR - IF BP(t) + CoC (t)

expected net income = IF BP(t) + i(t) * RC(t-1)

Then use CoC(t) = [RDR - i(t)] * RC(t-1)

Then put it all together

IBV(t-1) x RDR - IF BP(t) + [RDR - i(t)] * RC(t-1)
+
IF BP(t) + i(t) * RC(t-1)

(the book profits and the i*RC terms fall out and you are left with your answer)

= IBV(t-1) x RDR + RDR * RC(t-1)
- IF BP(t) + IF BP(t)
- i(t) * RC(t-1) + i(t) * RC(t-1)
=[IBV(t-1) + RC(t-1)] * RDR

I hope that helps you.

-Dustin

 fightinphilz 06-23-2020 10:37 PM

Thanks Dustin, that helps. Now i see what's going on: They are adding together the expected contribution from the IBV and NI columns together to get the overall expected contribution from in-force and from new business, so like you said some terms cancel out and the formula simplifies.

so i guess my only question then is, in the SOA sample solution it labels row 6 as Target IBV and then row 8 as Ending IBV, but aren't those labels not accurate? Those would be the labels if we just had an IBV column. Typically I see the analysis of movement table broken out as having 2 columns, one for IBV and one for NI. so here if they are combining the two columns, row 6 should be labeled "Target IBV + Target NI" and row 8 should read "Closing IBV + Closing NI". This is especially troubling because the problem itself asks only for the AoM exhibit for IBV. Isn't the way the SOA is asking this question very misleading given that they ask for AoM for only IBV?

 All times are GMT -4. The time now is 09:03 PM.