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

BattleTable

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

• case O/S method 2 (formula) - for calculating ultimate / unpaid / IBNR
• case O/S method 1 (hard) - for calculating ultimate / unpaid / IBNR

reference	part (a)	part (b)	part (c)	part (d)
E (2019.Fall #18)	method 1 (hard): - calc unpaid	scenario where it works: - case O/S method
E (2017.Fall #22)	method 2 (formula): - calc unpaid	identify limitations: - in method for part (a)
E (2017.Spring #19)	expctd incremental clms: - rptd devlpt method	expctd incremental clms: - paid to prior case O/S	RY versus AY: - case O/S method
E (2016.Fall #19)	method 2 (formula): - calc unpaid	industry benchmarks: - reasonable?	unpaid estimate: - reasonable?
E (2016.Spring #17)	method 1 (hard): - calc unpaid	Case O/S method: -appropriate for part (a)?
E (2014.Spring #23)	cumulative % rptd: - calculate	method 2 (formula): - calc unpaid
E (2013.Spring #17)	method 2 (formula): - calc unpaid	identify limitations: - case O/S method	scenario where it works: - case O/S method

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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)

Case O/S method #1 uses a company's own data and reminds me of the frequency-severity disposal rate method. Lots of triangles, lots of judgmental selections. The method generally starts 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   =   (reported loss) – (paid loss)

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

Pop Quiz A!    :-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 be accurate in either of the above 2 situations?

Click for Answer 

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 feel 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:

Step 1

• calculate IPL (Incremental Paid Loss)

Step 2

Step 2a: calculate & make selections for: (current case O/S) ÷ (prior case O/S)

Step 2b: project case O/S using selections from step 2a

(The selections you make in step 2a are also called: remaining-in-case)

Step 3

Step 3a: calculate & make selections for: (current IPL) ÷ (prior case)

Step 3b: project IPL using selections from step 3a

(The selections you make in step 3a are also called: paid-on-case)

Final Step

• 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.)

E (2019.Spring #15)

Solution: 2019.Fall #20

Practice: 2 problems like 2019.Fall #20

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.

E (2016.Spring #17)

And the quiz. ("Would that this hoodie were a time hoodie." ← shout-out to the first Battle-Axer who identifies the person who said this. Hint: Click here.)

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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 vacuum tube computers. Joking aside, there may actually be a few situations where historical paid losses are unavailable:

• Self-insured entities
• Older years
• After mergers

I sometimes think of this as the Society of Actuaries method because the hint for when we may have to use it is SOA. Actually, I think I might switch from CAS to SOA. 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.

case O/S factor    =    1   +   [ (rptd:CDF – 1)  x  paid:CDF ]  ⁄  (paid:CDF – rptd:CDF)

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

unpaid    =    (case O/S amount)   x   case O/S factor

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

rptd:CDF (industry)   =   1.1

paid:CDF (industry)   =   1.3

case O/S (company)   =   1,000

then

case O/S factor = 1 + (1.1 - 1) x 1.3 / (1.3 - 1.1) = 1.65

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:

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.

EXAMPLE:   Case O/S Method #2

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 self-insured and that was the tip-off to use case O/S method #2.)

E (2017.Fall #22)

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.

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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.

Case O/S Methods Key Assumptions: same assumptions as for any development method plus for case O/S method #1 → claims activity related to IBNR is related consistently to claims already reported for case O/S method #2 → 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 Chapter 2 - Components of the Unpaid Claim Estimate that IBNR can be separated into:

• IBNER (Incurred But Not Enough Reported or development on known claims)
• IBNYR (Incurred But Not Yet Reported or pure IBNR)

So saying that IBNR activity is related to claims already reported implies the method works best when there is no 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.

Question: in what situations 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^st 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 not 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...

Question: identify disadvantages of the case O/S methods

Case O/S methods #1 & #2:

• selections for remaining-in-case and paid-on-case are not intuitive in the way that selection of development factors is intuitive, especially for tail factors
• selections for remaining-in-case and paid-on-case have no industry benchmarks for comparison to the actuary's selections
• projections of unpaid amounts can be distorted by case reserves for large losses
• not useful in estimating pure IBNR

Case O/S methods #2:

• industry CDFs may not be appropriate (especially for a self-insurer that may operate a unique line of business)
• industry CDFs for early maturities may be highly leveraged which may cause volatile projections of unpaid amounts

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

Question: in what situations is case O/S method #2 used because company data is limited [Hint: SOA]

• Self-insured entities
• Older years
• After mergers

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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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