Actuarial Outpost Expected Reinsurer Deficit
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#1
03-22-2012, 11:27 AM
 General Apathy Revered CAS AAA Join Date: Jun 2006 Location: St. Kitts Studying for the Beach Favorite beer: Carib Posts: 32,864
Expected Reinsurer Deficit

Help me settle a bet.

What is the ERD at the 99th percentile given the following data:

Percentile Loss
99.0% 4,799,769
99.1% 4,877,292
99.2% 4,982,982
99.3% 5,134,494
99.4% 5,401,793
99.5% 5,626,858
99.6% 5,803,433
99.7% 6,088,999
99.8% 6,476,636
99.9% 7,021,987
#2
03-22-2012, 11:38 AM
 Colymbosathon ecplecticos Member Join Date: Dec 2003 Posts: 5,813

Spoiler:
Odds are that you're wondering what to do with the first loss amount. The first term should be ((4,877,292 - 4,799,769)/2 + 4,799,769) *0.001, the trapezoid method. Other numerical methods could also be used, such as Simpson's Rule.

You will always have a problem with what to do at the other end. You might fit a curve in various ways, but I suspect that the bet is about whether to use the first point or not.

PS How did the world-wide roller-coaster tour work out?
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#3
03-22-2012, 12:04 PM
 tommie frazier Member Join Date: Aug 2003 Favorite beer: The kind with 2 e's Posts: 22,694

the loss there is the reinsurer's loss?

idk, like 56k?
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#4
03-22-2012, 12:14 PM
 General Apathy Revered CAS AAA Join Date: Jun 2006 Location: St. Kitts Studying for the Beach Favorite beer: Carib Posts: 32,864

Code:
```                      Deficit		Average Defecit
99.0%	4,799,769			912,950
99.1%	4,877,292	77,523		Probability
99.2%	4,982,982	183,213		1%
99.3%	5,134,494	334,725		Expected Deficit
99.4%	5,401,793	602,024		9,130
99.5%	5,626,858	827,089		Percent of Premium
99.6%	5,803,433	1,003,664		0.190%
99.7%	6,088,999	1,289,230
99.8%	6,476,636	1,676,867
99.9%	7,021,987	2,222,218```
This is how I set it up. ERD of .19%.

is this way off? My brain doesn't work today.
#5
03-22-2012, 12:19 PM
 MountainHawk Member CAS AAA Join Date: Dec 2001 Location: Salem, MA Studying for Nothing!!!! College: Lehigh University Alum Favorite beer: Yuengling Posts: 64,850

That's if the premium = 99%ile.

I didn't think ERD had a percentile. It's just integral (0,infinity) of Pr(Loss) max(Loss-Premium,0) dLoss

Your calculation is an estimate of it if the Premium is 4,799,769.
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#6
03-22-2012, 12:21 PM
 General Apathy Revered CAS AAA Join Date: Jun 2006 Location: St. Kitts Studying for the Beach Favorite beer: Carib Posts: 32,864

Quote:
 Originally Posted by MountainHawk That's if the premium = 99%ile. I didn't think ERD had a percentile. It's just integral (0,infinity) of Pr(Loss) max(Loss-Premium,0) dLoss Your calculation is an estimate of it if the Premium is 4,799,769.
Yes sorry. I meant if the premium was 4,799,769...
#7
03-22-2012, 01:51 PM
 Klaymen Member CAS Join Date: Oct 2001 Studying for the Last Reformation Posts: 19,003

Hope you aren't writing Exam 9 questions
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#8
03-22-2012, 03:06 PM
 Doctor Who Member Join Date: Nov 2009 Posts: 22,943

Nah, he's going to write questions for the SOA.
#9
03-22-2012, 03:08 PM
 M^3 Member CAS Join Date: Jun 2010 Posts: 431

As MH mentioned, ERD doesn't have a percentile. Also, remember to put everything on a PV basis.
#10
03-22-2012, 03:12 PM
 MountainHawk Member CAS AAA Join Date: Dec 2001 Location: Salem, MA Studying for Nothing!!!! College: Lehigh University Alum Favorite beer: Yuengling Posts: 64,850

Quote:
 Originally Posted by M^3 As MH mentioned, ERD doesn't have a percentile. Also, remember to put everything on a PV basis.
PV? Interest rates are 0, done.
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