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#1
09-22-2019, 11:59 PM
 Kely Member SOA Join Date: Sep 2017 Location: Shenzhen, China College: The University of Iowa Alumni Posts: 39
STAM Sample Questions #321

Normally, earned premium is related with AY, not CY. But in this question, the solution treats earned premium in CY1 as in AY1. I think CY is each disgonal in the cumulative loss payment rectangle. Can anyone help me with that issue? Thanks!
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#2
10-02-2019, 08:11 PM
 gauchodelpaso Member SOA Join Date: Feb 2012 College: Eastern Michigan U Posts: 188

I believe you are correct. Reserves are normally calculated by AY. The examples in Brown's text do BF for a given AY and use Earned Premiums and ELRs by AY. It's odd that the official solution and a couple more I've seen disregard completely the notion and use earned premium for CY as it were for AY. It may just be another approximation, as it's the only data available. Or perhaps some of the rules used for workmen's compensation. Or something very basic we are missing.

Let's say we have 1 year single policy written on 1/1/2015. Total premium \$1200. By the end of 2015 the premium will be fully earned So EP(2015)=1200. We report an accident occurred on 7/1/2015. I may have a claim of 250 in each 2015, 150 in 2016, and 50 in 2017. Let's say that ELR is 60%. Using the Loss Ratio Method, I would estimate the total losses at 1200*0.6 = 720, of which I paid 450. So my reserves would be 720-450=270. Notice that I used the earned premium for CY2015.

Now if the policy was written on 4/1/2015, by the end of 2015 the EP'(2015)=900, and the results would be different.

Hopefully one of the gurus here may clarify the point.
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#3
10-02-2019, 08:30 PM
 Abraham Weishaus Member SOA AAA Join Date: Oct 2001 Posts: 7,261

There is no such thing as premium by AY. AY is only for accidents. Loss payments are categorized based on the year of the underlying accident. They may also be categorized by calendar year, but this is useful only for creating loss triangles - and then they would be classified both by calendar year and by accident year.

A premium, on the other hand, is not directly related to any accident, so it wouldn't make any sense to talk about the accident year of a premium. Many policies have no accidents at all.

Losses in AYx are compared to earned premiums in CYx. A loss in AYx relates to an accident that occurred in CYx, and that accident was on a policy that was in force at the time of the accident, and the premiums earned in CYx are what made the policy in force and the insurance company liable to pay for the accident.

Last edited by Abraham Weishaus; 10-03-2019 at 10:29 AM..
#4
10-02-2019, 10:39 PM
 gauchodelpaso Member SOA Join Date: Feb 2012 College: Eastern Michigan U Posts: 188

Thank you Dr Weishaus.

For some strange reason I thought that for each accident we had to see how much of the premium was earned, but then, as time passes, I could see that eventually the premium would be fully earned.

So if understand this right, we don't need to correlate the claims to each policy at all. We dump in a big bucket all the earned premiums for that year (and the corresponding ELR), and in another bucket the calculation for the ultimate losses for each AY corresponding to each CY. IBNR reserve in this case for BF for each AY is Ultimate losses * (1-1/fult).
What is confusing is that the answer in the exam labeled each year as CY instead of AY.
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#5
10-04-2019, 10:56 AM
 JZSportswhiz SOA Join Date: Aug 2017 College: University of Minnesota - Twin Cities Posts: 6

Where were you able to find the SOA solutions for questions 307 thru 329? For some reason everytime I click it thru the SOA site it only goes up to #307
#6
10-04-2019, 12:58 PM
 gauchodelpaso Member SOA Join Date: Feb 2012 College: Eastern Michigan U Posts: 188

JZSportswhiz I've got them there, perhaps your cookies may be acting up? Look in the syllabus

https://www.soa.org/globalassets/ass...-solutions.pdf

BTW they are numbered up to 328, not 329
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VEE: Economics - Corporate Finance - Applied Statistics

Last edited by gauchodelpaso; 10-04-2019 at 01:03 PM..
#7
10-04-2019, 03:28 PM
 JZSportswhiz SOA Join Date: Aug 2017 College: University of Minnesota - Twin Cities Posts: 6

Quote:
 Originally Posted by gauchodelpaso JZSportswhiz I've got them there, perhaps your cookies may be acting up? Look in the syllabus https://www.soa.org/globalassets/ass...-solutions.pdf BTW they are numbered up to 328, not 329
Ya that is very strange. This worked tho! Thanks a bunch!
#8
10-04-2019, 03:52 PM
 gauchodelpaso Member SOA Join Date: Feb 2012 College: Eastern Michigan U Posts: 188

Quote:
 Originally Posted by JZSportswhiz Ya that is very strange. This worked tho! Thanks a bunch!
you are quite welcome
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German
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Prelims: 1/P - 2/FM - 3F/MFE - LTAM - STAM
VEE: Economics - Corporate Finance - Applied Statistics
#9
07-19-2020, 01:44 AM
 joelcheung SOA Join Date: Mar 2018 Location: Singapore Studying for Exam STAM College: Singapore Management University, sophomore Posts: 13

STAM Sample Question 321
For this question, why is it that the f(ult) factor is larger for the later expected losses? Shouldn't it be the case that the earlier expected losses (say those in CY1 and CY2) have a higher f(ult) as compared to that in CY3?

It seems as though that the expected losses at CY3 has to be trended and developed from year 1 while that of CY1 is only trended from year 3 and ignores any development from 12 to 24 months and 24 to 26 months.

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