Actuarial Outpost
 
Go Back   Actuarial Outpost > Exams - Please Limit Discussion to Exam-Related Topics > SoA/CAS Preliminary Exams > Exam 4/C - Construction and Evaluation of Actuarial Models
FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

2017 ACTUARIAL SALARY SURVEYS
Contact DW Simpson for a Personalized Salary Survey

Reply
 
Thread Tools Search this Thread Display Modes
  #1  
Old 05-20-2018, 10:42 PM
RockOn RockOn is offline
Member
SOA
 
Join Date: Dec 2013
Studying for Exam C
Favorite beer: Polygamy Porter
Posts: 53
Default SOA #65

Hello!
A quick question about Non-Poisson frequency and classical credibility:

For this question I tried to use the following formula from the ASM manual table: 42.1

n0 * ((Var(n)/E[N]) + (Var(s)/(E[x]^2))

Where N represents frequency and x represents severity. However the SOA solution uses another formula to get the full credibility value:

n0 * (Var(S))

Where:
Var(s) = E[N] * Var(x) + Var(N) * (E[x])^2

Can someone explain why the second formula be used and not the first to calculate the full credibility value? Is there something in the wording of the problem?

Thank you for your help!
__________________
EXAMS: P | FM | MFE | MLC | C | PA |
VEE: ECON | STATS | CORP FINANCE |
FAP: MOD 1| MOD 2| MOD 3| MOD 4| MOD 5| IA| MOD 6| MOD 7| MOD 8| FA |
Reply With Quote
  #2  
Old 05-21-2018, 09:50 AM
Jim Daniel's Avatar
Jim Daniel Jim Daniel is offline
Member
SOA
 
Join Date: Jan 2002
Location: Davis, CA
College: Wabash College B.A. 1962, Stanford Ph.D. 1965
Posts: 2,617
Default

This is the danger in memorizing a bunch of different formulas for the full credibility standard for different cases---you get confused about which to use where.

For full credibility for a random variable W, the minimum number of _observations_ of W for full credibility is

(y / k)^2 Var[W] / E[W]^2.

In #65, my W is aggregate severity (denoted by X in the problem), and you have 2500 observations of the value of aggregate severity.

The formula you were applying inappropriately is for the minimum (expected) number of claims for full credibility for aggregate severity rather than for the minimum number of observations of aggregate severity.
__________________
Jim Daniel
Jim Daniel's Actuarial Seminars
www.actuarialseminars.com
jimdaniel@actuarialseminars.com
Reply With Quote
  #3  
Old 05-22-2018, 10:50 AM
RockOn RockOn is offline
Member
SOA
 
Join Date: Dec 2013
Studying for Exam C
Favorite beer: Polygamy Porter
Posts: 53
Default

Thank you for the reply!
Yes, that is a subtlety that was lost on me.

I was thinking about the 2500 - not as observations but as exposures...

I think I need to study this further as I'm not sure I fully understand it yet.

Thank you again!
__________________
EXAMS: P | FM | MFE | MLC | C | PA |
VEE: ECON | STATS | CORP FINANCE |
FAP: MOD 1| MOD 2| MOD 3| MOD 4| MOD 5| IA| MOD 6| MOD 7| MOD 8| FA |
Reply With Quote
  #4  
Old 05-22-2018, 11:07 AM
Jim Daniel's Avatar
Jim Daniel Jim Daniel is offline
Member
SOA
 
Join Date: Jan 2002
Location: Davis, CA
College: Wabash College B.A. 1962, Stanford Ph.D. 1965
Posts: 2,617
Default

Quote:
Originally Posted by RockOn View Post
Thank you for the reply!
Yes, that is a subtlety that was lost on me.

I was thinking about the 2500 - not as observations but as exposures...

I think I need to study this further as I'm not sure I fully understand it yet.

Thank you again!
That basic formula always gives you the minimum number of observations of W. You just have to ask yourself “when do I observe a value of W?” When W is frequency or aggregate severity per exposure unit, the answer is “every time an exposure unit goes by”. When W is severity per accident, the answer is “every time an accident occurs”.
__________________
Jim Daniel
Jim Daniel's Actuarial Seminars
www.actuarialseminars.com
jimdaniel@actuarialseminars.com
Reply With Quote
Reply

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

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 07:58 PM.


Powered by vBulletin®
Copyright ©2000 - 2018, 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 0.21649 seconds with 9 queries