Actuarial Outpost MII (A + da = 1)
 User Name Remember Me? Password
 Register Blogs Wiki FAQ Calendar Search Today's Posts Mark Forums Read
 FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

 United KingdomActuarial Jobs General Insurance, Life & Other Areas Canada Actuarial JobsCasualty, Life,Pension,Health & Investment Entry LevelActuarial JobsAll Disciplines Health, Life, Pension, Casualty, Investment D.W. Simpson & Company ActuarialRecruitersWorldwide www.dwsimpson.com

 Thread Tools Display Modes
#1
04-22-2004, 12:43 PM
 Brutè Member Join Date: Dec 2001 Location: The 'shoe Posts: 2,330
MII (A + da = 1)

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 + ...)
#2
04-22-2004, 04:28 PM
 E Eddie Smith SOA AAA Join Date: May 2003 Location: Geographically, the Southeast, but virtually, everywhere. College: UGA Posts: 8,013

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.
#3
04-22-2004, 05:30 PM
 Sunny Member Join Date: Nov 2003 Posts: 3,940

Quote:
 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....
#4
04-23-2004, 08:57 AM
 funk1 Member Join Date: Oct 2003 Location: Post Exam C Coma Posts: 1,054

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.
#5
04-25-2004, 07:49 PM
 Sunny Member Join Date: Nov 2003 Posts: 3,940

Again, question here, do you mean from WL to WL annuity and term benefit to term annuity? I'm lost!
#6
04-26-2004, 03:15 PM
 Jim Daniel Member SOA Join Date: Jan 2002 Location: Davis, CA College: Wabash College 1962 (!) Posts: 1,732

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
__________________
Jim Daniel
Jim Daniel's Actuarial Seminars
www.actuarialseminars.com
jimdaniel@actuarialseminars.com
#7
04-26-2004, 11:11 PM
 Sunny Member Join Date: Nov 2003 Posts: 3,940

Thank you!

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off

All times are GMT -4. The time now is 04:33 AM.

 -- Default Style - Fluid Width ---- Default Style - Fixed Width ---- Old Default Style ---- Easy on the eyes ---- Smooth Darkness ---- Chestnut ---- Apple-ish Style ---- If Apples were blue ---- If Apples were green ---- If Apples were purple ---- Halloween 2007 ---- B&W ---- Halloween ---- AO Christmas Theme ---- Turkey Day Theme ---- AO 2007 beta ---- 4th Of July Contact Us - Actuarial Outpost - Archive - Privacy Statement - Top

Powered by vBulletin®
Copyright ©2000 - 2013, Jelsoft Enterprises Ltd.
*PLEASE NOTE: Posts are not checked for accuracy, and do not
represent the views of the Actuarial Outpost or its sponsors.
Page generated in 0.34779 seconds with 7 queries