View source for Friedland12.CaseOS

'''Reading''': Friedland, J.F., Estimating Unpaid Claims Using Basic Techniques, Casualty Actuarial Society, Third Version, July 2010. The Appendices are excluded.

'''Chapter 12''': Case Outstanding Development Method

==Pop Quiz==

* Identify the key <u>assumption</u> for the development method.
* identify <u>situations</u> where the development method is likely to work well.

: <span style="background-color: lightblue; border-radius: 5px;"> ''[[Friedland12.CaseOS#POP_QUIZ_ANSWERS |Click for Answer]]''&nbsp;</span>

==Study Tips==

==BattleTable==

Based on past exams, the '''main things''' you need to know ''(in rough order of importance)'' are:

* <span style="color: green;">'''case O/S method 2 (formula)'''</span> - for calculating ultimate / unpaid / IBNR
* <span style="color: blue;">'''case O/S method 1 (hard)'''</span> - for calculating ultimate / unpaid / IBNR

: {| class='wikitable' style='width: 1000px;'

|-
! style='width: 175px;' | reference !! style='width: 175px;' | part (a) !! style='width: 175px;' | part (b) !! style='width: 175px;' | part (c) !! part (d)

|-
|| [https://www.battleacts5.ca/pdf/Exam_(2019_2-Fall)/(2019_2-Fall)_(18).pdf <span style='font-size: 12px; background-color: yellow; border: solid; border-width: 1px; border-radius: 5px; padding: 2px 5px 2px 5px; margin: 5px;'>E</span>] <span style="color: red;">'''(2019.Fall #18)'''</span>
|| <span style="color: blue;">'''method 1 (hard):'''</span> <br> - calc unpaid
|| '''scenario where it works''': <br> - case O/S method
| style="background-color: lightgrey;" | 
| style="background-color: lightgrey;" | 

|-
|| [https://www.battleacts5.ca/pdf/Exam_(2017_2-Fall)/(2017_2-Fall)_(22).pdf <span style='font-size: 12px; background-color: yellow; border: solid; border-width: 1px; border-radius: 5px; padding: 2px 5px 2px 5px; margin: 5px;'>E</span>] <span style='color: red;'>'''(2017.Fall #22)'''</span>
|| <span style="color: green;">'''method 2 (formula):'''</span> <br> - calc unpaid
|| '''identify limitations''': <br> - in method for part (a)
| style="background-color: lightgrey;" | 
| style="background-color: lightgrey;" | 

|-
|| [https://www.battleacts5.ca/pdf/Exam_(2017_1-Spring)/(2017_1-Spring)_(19).pdf <span style='font-size: 12px; background-color: yellow; border: solid; border-width: 1px; border-radius: 5px; padding: 2px 5px 2px 5px; margin: 5px;'>E</span>] <span style='color: red;'>'''(2017.Spring #19)'''</span>
|| '''expctd incremental clms''': <br> - rptd devlpt method
|| '''expctd incremental clms''': <br> - paid to prior case O/S
|| '''RY versus AY''': <br> - case O/S method
| style="background-color: lightgrey;" | 

|-
|| [https://www.battleacts5.ca/pdf/Exam_(2016_2-Fall)/(2016_2-Fall)_(19).pdf <span style='font-size: 12px; background-color: yellow; border: solid; border-width: 1px; border-radius: 5px; padding: 2px 5px 2px 5px; margin: 5px;'>E</span>] <span style='color: red;'>'''(2016.Fall #19)'''</span>
|| <span style="color: green;">'''method 2 (formula):'''</span> <br> - calc unpaid
|| '''industry benchmarks''': <br> - reasonable?
|| '''unpaid estimate''': <br> - reasonable?
| style="background-color: lightgrey;" | 

|-
|| [https://www.battleacts5.ca/pdf/Exam_(2016_1-Spring)/(2016_1-Spring)_(17).pdf <span style='font-size: 12px; background-color: yellow; border: solid; border-width: 1px; border-radius: 5px; padding: 2px 5px 2px 5px; margin: 5px;'>E</span>] <span style='color: red;'>'''(2016.Spring #17)'''</span>
|| <span style="color: blue;">'''method 1 (hard):'''</span> <br> - calc unpaid
|| '''Case O/S method''': <br> -appropriate for part (a)?
| style="background-color: lightgrey;" | 
| style="background-color: lightgrey;" | 

|-
|| [https://www.battleacts5.ca/pdf/Exam_(2014_1-Spring)/(2014_1-Spring)_(23).pdf <span style='font-size: 12px; background-color: yellow; border: solid; border-width: 1px; border-radius: 5px; padding: 2px 5px 2px 5px; margin: 5px;'>E</span>] <span style='color: red;'>'''(2014.Spring #23)'''</span>
|| '''cumulative % rptd''': <br> - calculate
|| <span style="color: green;">'''method 2 (formula):'''</span> <br> - calc unpaid
| style="background-color: lightgrey;" | 
| style="background-color: lightgrey;" | 

|-
|| [https://www.battleacts5.ca/pdf/Exam_(2013_1-Spring)/(2013_1-Spring)_(17).pdf <span style='font-size: 12px; background-color: yellow; border: solid; border-width: 1px; border-radius: 5px; padding: 2px 5px 2px 5px; margin: 5px;'>E</span>] <span style='color: red;'>'''(2013.Spring #17)'''</span>
|| <span style="color: green;">'''method 2 (formula):'''</span> <br> - calc unpaid
|| '''identify limitations''': <br> - case O/S method
|| '''scenario where it works''': <br> - case O/S method
| style="background-color: lightgrey;" | 

|}

[https://www.battleacts5.ca/FC.php?selectString=**&filter=both&sortOrder=natural&colorFlag=allFlag&colorStatus=allStatus&priority=importance-high&subsetFlag=miniQuiz&prefix=Friedland12&suffix=CaseOS&section=all&subSection=all&examRep=all&examYear=all&examTerm=all&quizNum=all<span style="font-size: 20px; background-color: lightgreen; border: solid; border-width: 1px; border-radius: 10px; padding: 2px 10px 2px 10px; margin: 10px;">'''Full BattleQuiz]'''</span> <span style="color: red;">'''You must be <u>logged in</u> or this will not work.'''</span>

==In Plain English!==

There are 2 case O/S ''(case outstanding)'' methods and we discuss the hard method first. That normally wouldn't be logical but the 2 methods are not very similar, other than that they both used case O/S data in some way. So from the point of view of learning, there's no advantage in covering the easy method first. Let's just get the hard one out of the way first.

===Case O/S Method #1 (Hard Method)===

This case O/S method is sometimes referred to as a '''development method''' because step 2 ''(see further down)'' looks at how case O/S develops from one period to the next. Case O/S method #1 uses a '''company's own data'''  and reminds me of the ''[[Friedland11.FreqSev#Example_D:_Method_.233_-_Disposal_Rate_Method | frequency-severity disposal rate method]]''. Lots of triangles, lots of judgmental selections. The method generally <u>starts</u> with 2 triangles:

* paid loss ''(either cumulative or incremental)''
* case O/S loss

It doesn't matter whether the given paid losses are cumulative or incremental because you can calculate one from the other. Recall also:

* case O/S loss &nbsp; = &nbsp; (reported loss) &ndash; (paid loss)

So this method uses <u>both</u> paid & reported data. That might not be a good thing. Alice has a pop quiz and morality tale for you.

{| class="wikitable"
|-
| style="background-color: darkslategrey; color: white; border: solid; border-width: 2px; border-radius: 10px;" | '''Pop Quiz A! &nbsp;&nbsp; :-o'''
|}

: '''(a)''' Would you expect methods using unadjusted paid data to be accurate when there has been a change in the settlement rate of claims?
: '''(b)''' Would you expect methods using unadjusted reported data to be accurate when there has been a change in case reserve adequacy?
: '''(c)''' Based on your answers to (a) and (b), would you expect case O/S method #1 to be accurate in either of the above 2 situations?

: <span style="background-color: lightblue; border-radius: 5px;"> ''[[Friedland12.CaseOS#Pop_Quiz_A_-_ANSWER |Click for Answer]]''&nbsp;</span>

{| class='wikitable' style='width: 1000px;'
|-
|| '''Alice's Morality Tale''': The more complicated a method is, the more ways it can fail. It's true that more sophisticated methods allow the actuary to make explicit assumptions for things like inflation, frequency & severity trends, court decisions, and probably many others, but each additional assumption magnifies the parameter risk. That's why the good old development method is so common. Reserving methods that simply pile on the parameters make you <u>feel</u> like they must be more accurate, but at some point they are subject to the law of diminishing returns.
|}

Assuming you're given CPL ''(Cumulative Paid Loss)'' and case O/S loss, here are the steps for case O/S method #1:

<span style="color: brown;>'''<u>Step 1</u>'''</span>

* calculate IPL ''(Incremental Paid Loss)''

<span style="color: brown;>'''<u>Step 2</u>'''</span>

: '''Step 2a''': calculate & make selections for:  '''(current case O/S) &#247; (prior case O/S)''' &nbsp;&nbsp; <span style="color: red;>&larr; ''this is why it's sometimes called a development method''</span>
: '''Step 2b''': project <u>case O/S</u> using selections from step 2a
: ''(The <u>selections</u> you make in step 2a are also called: remaining-in-case)''

<span style="color: brown;>'''<u>Step 3</u>'''</span>

: '''Step 3a''': calculate & make selections for:  '''(current IPL) &#247; (prior case)'''
: '''Step 3b''': project <u>IPL</u> using selections from step 3a
: ''(The <u>selections</u> you make in step 3a are also called: paid-on-case)''

<span style="color: brown;>'''<u>Final Step</u>'''</span>

* sum IPL as appropriate to calculate either ultimate or unpaid amounts

Here's an exam problem based on this idea along with Alice's solution and a couple of practice problems. ''('''Note''': Sample answer 1 in the examiner's report has an error in the next-to-last step where they calculate paid-on-case for different ages. The values for 12, 36, and 48 months are incorrect and the value for 60 months is missing. See Alice's solution for the correct values.)''

: [https://www.battleacts5.ca/pdf/Exam_(2019_2-Fall)/(2019_2-Fall)_(18).pdf <span style='font-size: 12px; background-color: yellow; border: solid; border-width: 1px; border-radius: 5px; padding: 2px 5px 2px 5px; margin: 5px;'>E</span>] <span style="color: red;">'''(2019.Fall #18)'''</span>

: [https://www.battleacts5.ca/pdf/F-12_(010)_COS_2019_Fall_Q18.pdf <span style="color: white; font-size: 12px; background-color: orchid; border: solid; border-width: 2px; border-radius: 10px; border-color: orchid; padding: 1px 3px 1px 3px; margin: 0px;">'''''Solution: 2019.Fall #18'''''</span>]

: [https://www.battleacts5.ca/pdf/F-12_(010)_COS_method_1.pdf <span style="color: white; font-size: 12px; background-color: green; border: solid; border-width: 2px; border-radius: 10px; border-color: green; padding: 1px 3px 1px 3px; margin: 0px;">'''''Practice: 2 problems like 2019.Fall #18'''''</span>]

This next exam problem uses the same method but it's an easier version because you are already given the selected factors from steps 2a and 3a. ''(You may need to come back to part (b) after you've covered [[Friedland12.CaseOS#Case_O.2FS_Method_Concepts | Case O/S Method Concepts]].)''

: [https://www.battleacts5.ca/pdf/Exam_(2016_1-Spring)/(2016_1-Spring)_(17).pdf <span style='font-size: 12px; background-color: yellow; border: solid; border-width: 1px; border-radius: 5px; padding: 2px 5px 2px 5px; margin: 5px;'>E</span>] <span style='color: red;'>'''(2016.Spring #17)'''</span>

And the quiz. ''("Would that this hoodie were a time hoodie." <span style="color: green;">&larr; shout-out to the first Battle-Axer who identifies the person who said this.</span> <span style="color: red;">'''Hint:'''</span> [https://www.youtube.com/watch?v=2Vy_wqPHxTI Click here.])''

[https://www.battleacts5.ca/FC.php?selectString=**&filter=both&sortOrder=natural&colorFlag=allFlag&colorStatus=allStatus&priority=importance-high&subsetFlag=miniQuiz&prefix=Friedland12&suffix=CaseOS&section=all&subSection=all&examRep=all&examYear=all&examTerm=all&quizNum=1<span style="font-size: 20px; background-color: aqua; border: solid; border-width: 1px; border-radius: 10px; padding: 2px 10px 2px 10px; margin: 10px;">'''mini BattleQuiz 1]'''</span> <span style="color: red;">'''You must be <u>logged in</u> or this will not work.'''</span>

===Case O/S Method #2 (Formula Method)===

Case O/S method #2 uses '''industry data''' to project a company's current case O/S amount. It's assumed that no other company data is available, which isn't common unless your IT department still uses ''[https://www.battleacts5.ca/images/eniac3.gif vacuum tube computers]''. Joking aside, there may actually be a few situations where historical paid losses are unavailable:

* <span style="color: red;">'''S'''</span>elf-insured entities
* <span style="color: red;">'''O'''</span>lder years
* <span style="color: red;">'''A'''</span>fter mergers

I sometimes think of this as the Society of Actuaries method because the hint for when we may have to use it is <span style="color: red;">'''SOA'''</span>. Actually, I think I might switch from CAS to SOA. ''[https://www.battleacts5.ca/images/SOA_dancing.png These guys]'' look like they're having a blast!

Here are the formulas you need. The reported and paid CDFs are derived from '''industry data'''.

:{| class='wikitable'
|-
|| '''case O/S factor''' &nbsp;&nbsp; = <span style="color: green;">'''&nbsp;&nbsp; 1 &nbsp; + &nbsp;'''</span> [ (rptd:CDF &ndash;  1) &nbsp;x&nbsp; <span style="color: red;">paid:CDF</span> ] &nbsp;&frasl;&nbsp; (<span style="color: red;">paid:CDF</span> &ndash; rptd:CDF)
|}

Then you simply multiply this factor by company case O/S amount to get the final unpaid amount.

:{| class='wikitable'
|-
|| '''unpaid''' &nbsp;&nbsp; = &nbsp;&nbsp; (case O/S amount) &nbsp; x &nbsp; '''case O/S factor'''
|}

As a very simple example, suppose we're given:

: '''rptd:CDF''' (industry) &nbsp; = &nbsp; 1.1
: '''paid:CDF''' (industry) &nbsp; = &nbsp; 1.3
: '''case O/S''' (company) &nbsp; = &nbsp; 1,000

then

: '''case O/S factor''' = 1 + (1.1 - 1) x 1.3 / (1.3 - 1.1) = <u>1.65</u>

and the final unpaid amount is:

: '''unpaid''' = 1,000 x 1.65 = '''1,650'''

Before moving on, Alice has something she wants to tell you:

:{| class='wikitable'
|-
|| '''Alice's Pro Tip for Case O/S Method #2''': Be careful to use the correct age-to-ultimate CDF for the AY you are projecting.
|}

Case O/S method #2 must be applied separately to each AY. Here's the example form the source text and it shows the method applied to 6 AYs in the same table. Just make sure you can follow the calculations. It's easy.

: [https://www.battleacts5.ca/pdf/Friedland.Ch12_(ex_20_CaseOS_2).pdf <span style="color: white; font-size: 12px; background-color: sandybrown; border: solid; border-width: 2px; border-radius: 10px; border-color: sandybrown; padding: 1px 3px 1px 3px; margin: 0px;">'''''EXAMPLE: &nbsp; Case O/S Method #2'''''</span>]

The exam problem below requires a little more work than the simple example above. They give you the industry reported CDF but you have to calculate the industry paid CDF yourself. Still, it isn't a hard problem. Give it a try. ''(Sample answer 1 in the examiner's report is the best answer. Sample answer 2 is valid but uses case O/S method #1, which probably received full credit but takes longer and was clearly not what the examiners intended. They told you the company was <u>self-insured</u> and that was the tip-off to use case O/S method #2.)''

: [https://www.battleacts5.ca/pdf/Exam_(2017_2-Fall)/(2017_2-Fall)_(22).pdf <span style='font-size: 12px; background-color: yellow; border: solid; border-width: 1px; border-radius: 5px; padding: 2px 5px 2px 5px; margin: 5px;'>E</span>] <span style='color: red;'>'''(2017.Fall #22)'''</span>

Part (b) of the question asks you to list limitations of case O/S method #2. We'll cover this in the next section but common sense tells you one limitation is that the industry LDFs may not be representative of this indivdual company.

[https://www.battleacts5.ca/FC.php?selectString=**&filter=both&sortOrder=natural&colorFlag=allFlag&colorStatus=allStatus&priority=importance-high&subsetFlag=miniQuiz&prefix=Friedland12&suffix=CaseOS&section=all&subSection=all&examRep=all&examYear=all&examTerm=all&quizNum=2<span style="font-size: 20px; background-color: aqua; border: solid; border-width: 1px; border-radius: 10px; padding: 2px 10px 2px 10px; margin: 10px;">'''mini BattleQuiz 2]'''</span> <span style="color: red;">'''You must be <u>logged in</u> or this will not work.'''</span>

===Case O/S Method Concepts===

As always, we need to know the assumptions underlying the method. If the assumptions aren't satisfied then the method may give inaccurate results.

:{| class='wikitable'
|-
|| '''Case O/S Methods Key Assumptions''': same ''[[Friedland07.Development#Development_Method_-_The_Key_Assumption | assumptions as for any development method]]'' '''plus'''
: for case O/S method #1 &rarr; ''claims activity related to IBNR is related consistently to claims already reported''
: for case O/S method #2 &rarr; ''historical industry experience is indicative of future experience for the company''
|}

The source text elaborates on the assumption for case O/S method #1. Recall from ''[[Friedland02.ClmsProcess#Five_Components_of_the_Total_Unpaid_Claim_Estimate | Chapter 2 - Components of the Unpaid Claim Estimate]]'' that IBNR can be separated into:

* <u>IBNER</u> ''(Incurred But Not Enough Reported <u>or</u> development on known claims)''
* <u>IBNYR</u> ''(Incurred But Not Yet Reported <u>or</u> pure IBNR)''

So saying that IBNR activity is related to claims already reported implies the method works best when there is <u>no</u> IBNYR or pure IBNR. If there was a significant proportion of IBNYR, then these extra new claims in future development periods could distort the ''paid-to-case'' ratios used in method #1. You might have to sit in a dark room and think about that for a little while.

Now that we know the general assumptions underlying the case O/S methods, let's identify real-life situations where they are satisfied and where the case O/S method is likely to work well.

:{| class='wikitable'
|-
|| '''Question''': in what <u>general situations</u> are the key assumptions for the Case O/S methods more likely to be satisfied
|}

:* for AY triangles where most claims are reported by the 1<sup>st</sup> development period ''(because then there is probably only a small amount of pure IBNR)''
:* for report year triangles ''(because there is no pure IBNR)''
:* for claims-made policies ''(because there is no pure IBNR)''

:: ''(Case O/S methods are <u>not</u> extensively used by actuaries. Case O/S method #2 can be used when the only company data available is case O/S. In that situation, insufficient data is available for other methods.)''

And of course, you also need to memorize the answer to this...

:{| class='wikitable'
|-
|| '''Question''': identify <u>disadvantages</u> of the case O/S methods
|}

:: '''Case O/S methods #1 & #2''':
::* selections for ''remaining-in-case'' and ''paid-on-case'' are <u>not intuitive</u> in the way that selection of development factors is intuitive, especially for tail factors
::* selections for ''remaining-in-case'' and ''paid-on-case'' have <u>no industry benchmarks</u> for comparison to the actuary's selections
::* projections of unpaid amounts can be distorted by case reserves for <u>large losses</u>
::* not useful in estimating <u>pure IBNR</u>

:: '''Case O/S methods #2''':
::* industry CDFs <u>may not be appropriate</u> ''(especially for a self-insurer that may operate a unique line of business)''
::* industry CDFs for early maturities <u>may be highly leveraged</u> which may cause volatile projections of unpaid amounts

And here's a quick reminder from the beginning of the section on method #2:

:{| class='wikitable'
|-
|| '''Question''': in what <u>specific situations</u> is case O/S method #2 used because company data is limited [Hint: <span style="color: red;">'''SOA'''</span>]
|}

:* <span style="color: red;">'''S'''</span>elf-insured entities
:* <span style="color: red;">'''O'''</span>lder years
:* <span style="color: red;">'''A'''</span>fter mergers

Remember the dancing actuaries from above? If you feel like wasting 5 minutes, here's another ''[https://www.youtube.com/watch?v=TcWPiHjIExA dynamite dance scene]''. Don't forget to vote for Pedro.

[https://www.battleacts5.ca/FC.php?selectString=**&filter=both&sortOrder=natural&colorFlag=allFlag&colorStatus=allStatus&priority=importance-high&subsetFlag=miniQuiz&prefix=Friedland12&suffix=CaseOS&section=all&subSection=all&examRep=all&examYear=all&examTerm=all&quizNum=3<span style="font-size: 20px; background-color: aqua; border: solid; border-width: 1px; border-radius: 10px; padding: 2px 10px 2px 10px; margin: 10px;">'''mini BattleQuiz 3]'''</span> <span style="color: red;">'''You must be <u>logged in</u> or this will not work.'''</span>

===Extra Problems===

Just a couple of extra exam problems that didn't quite fit into any other category...

[https://www.battleacts5.ca/FC.php?selectString=**&filter=both&sortOrder=natural&colorFlag=allFlag&colorStatus=allStatus&priority=importance-high&subsetFlag=miniQuiz&prefix=Friedland12&suffix=CaseOS&section=all&subSection=all&examRep=all&examYear=all&examTerm=all&quizNum=4<span style="font-size: 20px; background-color: aqua; border: solid; border-width: 1px; border-radius: 10px; padding: 2px 10px 2px 10px; margin: 10px;">'''mini BattleQuiz 4]'''</span> <span style="color: red;">'''You must be <u>logged in</u> or this will not work.'''</span>

[https://www.battleacts5.ca/FC.php?selectString=**&filter=both&sortOrder=natural&colorFlag=allFlag&colorStatus=allStatus&priority=importance-high&subsetFlag=miniQuiz&prefix=Friedland12&suffix=CaseOS&section=all&subSection=all&examRep=all&examYear=all&examTerm=all&quizNum=all<span style="font-size: 20px; background-color: lightgreen; border: solid; border-width: 1px; border-radius: 10px; padding: 2px 10px 2px 10px; margin: 10px;">'''Full BattleQuiz]'''</span> <span style="color: red;">'''You must be <u>logged in</u> or this will not work.'''</span>

==POP QUIZ ANSWERS==

The answers can be found in ''[[Friedland07.Development#Development_Method_-_The_Key_Assumption | Chapter 7 - The Development Method Key Assumptions]]''.

:{| class='wikitable'
|-
|| '''Key Assumption:''' The development method assumes future loss development is <u>similar</u> to development in prior years
|}

:{| class='wikitable'
|-
|| '''Question:''' identify <u>situations</u> where the development method is likely to work well
|}

:* consistent claim processing
:* stable mix of types of claims
:* stable policy limits
:* stable reinsurance & retention limits
:* high frequency & low severity lines of business

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==Pop Quiz A - ANSWER==

: '''(a)''' Generally no. Unadjusted paid data may be distorted by changes in the settlement rate of claims.
: '''(b)''' Generally no. Unadjusted reported data may be distorted by changes in the case strength or case reserve adequacy.
: '''(c)''' Generally no. Since this case O/S method uses both paid and reported data, changes in both settlement rates and case strength may distort the inputs and therefore reduce the accuracy of the final estimates of ultimate.

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