Actuarial Outpost
 
Go Back   Actuarial Outpost > Actuarial Discussion Forum > Property - Casualty / General Insurance
FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

Actuarial Jobs by State

New York  New Jersey  Connecticut  Massachusetts 
California  Florida  Texas  Illinois  Colorado


Reply
 
Thread Tools Search this Thread Display Modes
  #1  
Old 12-31-2018, 12:08 AM
beanie beanie is offline
 
Join Date: Sep 2010
College: N/A
Posts: 10
Default Risk Margin - Bootstrapping Method

Bootstrapping is a common method used in estimating the volatility and risk margins assumptions.

Refering to the example below from this paper:
https://www2.math.su.se/matstat/repo...p13/report.pdf

Page 36 (Table 5)
Selected CoV = 20%, and assumed a lognormal distribution
BE Reserves = 4,175,994
75th percentile = 4,678,623 (Margin = 12.0%)
25th percentile = 3,584,941 (Margin = -14.2%)

I would like to find out the 60th percentile risk margin. Using the above example as illustration, I get a risk margin of 3.1%.

I also computed the 50th percentile risk margin as a sense check, which is -1.9%. Now this is where I have a question. I am expecting the 50th percentile risk margin to be close to zero, but it is negative. Intuitively, it does not make sense, but is this acceptable? Or do I have to somehow shift the lognormal distribution such that the 50th percentile is exactly 0%?

My concern is the 60th percentile risk margin is understated.
Reply With Quote
  #2  
Old 12-31-2018, 12:33 AM
Transitive Tangerine's Avatar
Transitive Tangerine Transitive Tangerine is offline
Member
COPA
 
Join Date: Oct 2018
Studying for FAP (hehehe nice)
Posts: 1,222
Default

Why do you expect it to be close to zero? What does the PDF of the lognormal look like?
Reply With Quote
  #3  
Old 12-31-2018, 12:50 PM
Harbinger Harbinger is offline
Notes Contributor
CAS
 
Join Date: Feb 2005
Posts: 2,408
Default

You’re confusing the 50th percentile with the mean. The lognormal distribution is often skewed right. It appears your mean is at the 51.9th percentile. You should not shift/adjust.
__________________
har·bin·ger (här'bin-jer): One that indicates or foreshadows what is to come; a forerunner.
Reply With Quote
  #4  
Old 01-01-2019, 12:30 PM
beanie beanie is offline
 
Join Date: Sep 2010
College: N/A
Posts: 10
Default

Quote:
Originally Posted by Harbinger View Post
You’re confusing the 50th percentile with the mean. The lognormal distribution is often skewed right. It appears your mean is at the 51.9th percentile. You should not shift/adjust.
You are right. Thank you!
Reply With Quote
  #5  
Old 01-01-2019, 09:30 PM
Harbinger Harbinger is offline
Notes Contributor
CAS
 
Join Date: Feb 2005
Posts: 2,408
Default

I meant 50.95th percentile, not 51.9th.
__________________
har·bin·ger (här'bin-jer): One that indicates or foreshadows what is to come; a forerunner.
Reply With Quote
  #6  
Old 01-02-2019, 09:45 AM
Transitive Tangerine's Avatar
Transitive Tangerine Transitive Tangerine is offline
Member
COPA
 
Join Date: Oct 2018
Studying for FAP (hehehe nice)
Posts: 1,222
Default

Quote:
Originally Posted by beanie View Post
You are right. Thank you!
np
Reply With Quote
  #7  
Old 01-02-2019, 12:23 PM
Westley Westley is offline
Member
 
Join Date: Nov 2001
Posts: 28,473
Default

Quote:
Originally Posted by Harbinger View Post
You’re confusing the 50th percentile with the mean. The lognormal distribution is often skewed right. It appears your mean is at the 51.9th percentile. You should not shift/adjust.


The fact that you (OP) were unclear on the need for adjustment means that it is likely that the reader/user is much MORE unclear, and calls for very careful communication/documentation.

Too many actuaries (not necessarily OP) worry about getting the numbers correct, and aren't concerned enough that they are *used* correctly.
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 05:10 AM.


Powered by vBulletin®
Copyright ©2000 - 2019, 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 0.15754 seconds with 9 queries