Friedland17.ULAE

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

Chapter 17: Estimating ULAE (UnAllocated Claim Adjustment Expenses)

Study Tips

VIDEO: F-17 (001) ULAE → 6:30 Forum

This chapter is 33 pages and covers many methods for calculating ULAE. But you can see from the BattleTable below that most of the calculation questions are about either the classical method or the Kittel refinement. These 2 methods are covered in just 8 pages in the source text.

Based on history, my recommendation is to study the mechanics of the classical and Kittel methods thoroughly, along with their assumptions, advantages & disadvantages. Then quickly learn the general theory behind the other methods. There's a web-based practice problem in quiz 5 at the bottom of this wiki article to help you with that. These other methods can address shortcomings of the classical and Kittel methods in certain specific situations. A great exam question illustrating that is (2017.Spring #24).

I've also included a couple of practice problems on the Conger-Nolibos method but that's less likely to show up on the exam.

Estimated study time: 2-3 days (not including subsequent review time)

BattleTable

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

• classical technique - calculation, assumptions, advantages & disadvantages
• Kittel refinement - calculation, assumptions, advantages & disadvantages

reference	part (a)	part (b)	part (c)	part (d)
E (2019.Fall #24)	Kittel refinement: - unpaid ULAE	calculation changes: - clms-made → occurrence
E (2018.Fall #22)	IBNYR claims: - calculate	any method: - unpaid ULAE
E (2018.Spring #23)      BattleActs PowerPack	classical technique: - unpaid ULAE	Kittel refinement: - unpaid ULAE	compare techniques: - classical vs Kittel
E (2017.Fall #26)	classical technique: - unpaid ULAE	calculate ratio: → (pd ULAE)/(pd claims)	assess reasonableness: - ULAE estimate
E (2017.Spring #24)	ULAE scenario: - expanding operations	ULAE scenario: - hurricane risk	ULAE scenario: - long-tail line
E (2016.Fall #26)	classical technique: - unpaid ULAE	classical technique: - assumption violation	Kittel refinement: - assess appropriateness
E (2016.Spring #22)	ALAE development: - unpaid ALAE	classical technique: - unpaid ULAE	assess reasonableness: - ULAE estimate
E (2015.Spring #25)	classical technique: - identify problem	Kittel refinement: - unpaid ULAE
E (2014.Fall #23)	B-F method: - claims IBNR	classical technique: - unpaid ULAE	classical technique: - assess assumptions	Kittel refinement: - describe
E (2013.Fall #19)	assess impact: - on ALAE ratio method	assess impact: - on ULAE Johnson method	assess impact: - on rates using PP method	assess impact: - on reinsurance recoverable
E (2013.Spring #25)	Kittel refinement: - unpaid ULAE	Kittel refinement: - purpose	classical technique: - shortcoming

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In Plain English!

Intro

This chapter covers many methods for estimating unpaid ULAE and there are 3 main categories:

1. Dollar-based methods:
   • classical method   ← heavily tested
   • Kittel refinement   ← heavily tested
   • Conger-Nolibos (generalized Kittel method)
   • Mango-Allen refinement
2. Count-based methods:
   • early methods used for ULAE (Brian method)
   • Wendy Johnson method
   • Mango-Allen claims staffing method
   • Rahardjo method
   • Spalla method
3. Triangle-based methods   ← rarely used by actuaries

We'll cover the mechanics for the classical method and Kittel refinement thoroughly. Then we'll cover the other methods in a more general way but based on past exams it's a lot less likely you would be asked to do a calculation using those other methods. It's important however to understand how they address shortcomings with the classical and Kittel methods.

Alice's Tip: Methods for calculating ULAE usually use CY data not AY data. This is because you cannot easily create an AY triangle for ULAE data. (More on this below.)

Keep Alice's Tip in the back of your mind as you work through this chapter.

Classical Method - General Formula

Take a moment to review What is ALAE & ULAE from the ALAE chapter of Friedland. Since ULAE isn't associated with a particular claim, there's no accident date or report date. So unlike ALAE data, you can't make a triangle for ULAE. But then what in the world do you do? Most reserving techniques are based on development triangles. With ULAE, there's a simple formula. Below is the classical version of the formula for unpaid ULAE. It's called a dollar-based method because the terms on the right side of the formula are all dollar amounts. The assumption is that ULAE payments track with claims payments in both timing and amount. Double your claim amounts → double your ULAE amounts. Do you think that's a good assumption? Alice-the Actuary doesn't. Recall that building rent is an example of ULAE so paying a $500 claim versus a $1,000 claim shouldn't make any difference to that. Or to make the point even clearer, ULAE on a $5,000 claim likely wouldn't be 10x the ULAE on a $500 claim. Later on we'll look at other methods that address shortcomings the classical method.

unpaid ULAE   =   (ULAE ratio)   x   [ 50% x (Case + IBNER)   +   100% x (IBNYR) ]

Case = Case Oustanding Claims Amount

IBNER = Incurred But Not Enough Reported

IBNYR = Incurred But Not Yet Reported (also called pure IBNR)

(Recall: Total IBNR = IBNER + IBNYR)

Example: Let's calculate the unpaid ULAE for calendar year 2021 given the following information:

• For the (ULAE ratio) we'll need some information from prior years:

paid ULAE (CY 2016 - 2020) = 110

paid claims (CY 2016 - 2020) = 1000

→ (ULAE ratio) = 110/1000 = 11%

• For CY 2021, you also need:

case = 300

IBNER = 120

IBNYR = 80

Then just substitute into the given formula:

unpaid ULAE

= 11% x [ 50% (300 + 120) + 100% x 80 ]

= 11% x 290

= 31.9

Pop Quiz A!    :-o

• Calculate the unpaid ULAE for CY 2021 using the method from above. Click for Answer 

paid ULAE (CY 2016 - 2020)	30
paid claims (CY 2016 - 2020)	200
case2021	500
IBNER2021	100
IBNYR2021	25

Classical Method - Simplified Formula

The ULAE formula from the previous section is sometimes written in a simpler way when you only have Total IBNR. In other words, if IBNR is not separated into IBNER and IBNYR, then you can assume all the IBNR is IBNYR or pure IBNR. The ULAE formula then collapses to:

unpaid ULAE   =   (ULAE ratio)   x   [ 50% x Case   +   100% x IBNR ]

Most of the old exam problems don't split IBNR into IBNER and IBNYR, but sometimes they do so you should be familiar with both versions of the formula. Anyhow, here are the assumptions underlying the formula:

stability assumption: the ratio (paid ULAE) / (paid claims) is stable and reasonably approximates the ratio (ultimates ULAE) / (ultimate claims)

proportionality assumption: the future cost for reported claims is proportional to the CASE AMOUNT, and the future cost of unreported claims is proportional to IBNR

The stability assumption means that if the ULAE ratio = (paid ULAE) / (paid claims) = 15%, then for every $100 of paid claims, the insurer will ultimately pay $15 of ULAE. But the above formula is for unpaid ULAE and the proportionality assumption tells you where this future unpaid ULAE will come from.

Let's try to think through why this makes sense. On a very simple level, when a claim is reported someone answers the phone, enters the claims into the system, and an adjuster may investigate the claim and set a reserve. This is all part of ALAE because it's directly associated with a particular claim. But at the same time the insurer is paying rent on their building, maintaining their computer systems, and various other things – all things they would have to do regardless of whether there's a claim. That's part of ULAE.

• If a claim has not been reported then no ULAE has been paid. In other words all of that ULAE is unpaid and the ULAE ratio is applied to 100% of unreported & unpaid claims or IBNR.
• If a claim has been reported with a case reserve then some portion of the ULAE has already been paid (we assume 50%, see below) so the unpaid ULAE for the reported claim is proportional to the unpaid portion of the claim, or in other words proportional to the case reserve.

But where does the value of 50% come from. This is just an assumption. According to the Friedland source text:

"The classical technique assumes that one-half of ULAE are sustained when opening a claim and one-half is sustained when closing the claim. Thus, we apply 50% of the ULAE ratio to case outstanding, since, for known claims, one-half of the unallocated work was already completed at the time of opening; and we apply 100% of the ULAE ratio to IBNR, since all unallocated work remains to be completed (that is, the work associated with opening and closing the claims)."

A shorter way of saying this is:

allocation assumption: (the Conger-Nolibos method allows adjustments to this 50/50 assumption)

• 50% of ULAE is sustained when a claim is reported
• 50% of ULAE is sustained when a claim is paid  ← this 50% is applied to CASE reserves because the case reserves is what will be paid

To summarize this section, you need to know both the basic version of the classical formula for unpaid ULAE as well as the simplified version. You should also understand and be able to state the assumptions behind the method.

Side note: This all made sense to me but then Alice pointed something out: It seems like this formula is in fact allocating ULAE to the report & payment of claims. But ULAE is supposed to represent unallocated expenses. (Shutup Alice!) I suppose the key point is that it isn't allocating it to specific claims, just the overall average what happened in the past.

Part (b) of the following exam problem is a really great question about the assumptions underlying the classical method:

E (2016.Fall #26)

Classical Method - Concepts

Now that you know how to calculate unpaid ULAE using the classical method and are aware of its assumptions, consider the following:

Question: identify situations where the classical method may not be appropriate [Hint: LIP-50]

Long-tail lines

Inflation

Premium growth (or shrinkage)

50/50 assumption not valid for insurer's claims handling workflow (different percentages might be appropriate)

You should also probably have some idea why these situations may distort the classical method.

• The first 3, LIP, are basically due to a mismatch between between (paid ULAE) and (paid claims) which distorts the ULAE ratio used in the formula. The issue is that paid ULAE could react differently to shocks than paid claims.

• With premium growth, paid ULAE may rise immediately, whereas paid claims incurs a lag so the ULAE ratio might be too high thus overestimating unpaid ULAE.
• With inflation, the rate may be different for (paid ULAE) versus (paid claims) which could cause over or under estimation of unpaid ULAE
• Long-tail lines of business (≥ 5 years) could be disproportionately impacted by inflation or other changes in internal or external conditions

• For the 50/50 assumption, this almost certainly will vary by insurer based on things like types of claims (long versus short tail lines) and the particular processes that a claim department actually uses.

Subtle point: The steady-state assumption (stability of the ULAE ratio) implies the further assumption that paid claims are approximately equal to reported claims, and thus the two quantities can be used interchangeably. If paid claims are indeed less than reported claims, the ULAE ratio could be initially over-estimated because those "extra" reported claims eventually become paid claims in the denominator of the ULAE ratio and will subsequently reduce the ULAE ratio.

The points above are essentially the disadvantages of the classical method. But if the classical method sucks so badly, why does anybody use it?

Question: identify advantages of the classical method

• easy to calculate
• data is usually available
• ULAE is usually a small percentage of total losses (a more complex method may be more accurate but the time & effort required may outweigh the benefit)

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Kittel Refinement

The source text makes the Kittel refinement seem a lot more complicated than it actually is because they show how it's derived mathematically. The only difference between the classical ULAE formula and the Kittel refinement is how the ULAE ratio is calculated. Just like the classical method, the Kittel refinement is a dollar-based method because all the terms on the right side of the formula are dollar amounts. The Kittel refinement addresses the shortcoming of the classical method when volume is growing or shrinking because it uses incurred claims not just paid claims. (Incurred claims are more responsive to changing volume than paid claims alone.)

Kittel ULAE ratio = (paid ULAE) / average(paid claims, incurred claims)

Example: This is the same example as in the first section, except we'll use the Kittel refinement instead of the classical technique. The extra piece of information we need to calculate the unpaid ULAE for 2021 using Kittel is highlighted in purple.

• For the (ULAE ratio) we'll need:

paid ULAE (CY 2016 - 2020) = 110

paid claims (CY 2016 - 2020) = 1000

incurred claims (CY 2016 - 2020) = 2000    ←    incurred claims include reported claims & IBNR

→ (ULAE ratio) = 110 / average(1000, 2000) = 7.3%

• For CY 2021 (as before):

case = 300

IBNER = 120

IBNYR = 80

Then just substitute into the classical method general formula:

unpaid ULAE

= 7.3% x [ 50% x (300 + 120) + 100% x 80 ]

= 7.3% x 290

= 21.2

(Note that this is lower than the value of 31.9 for unpaid ULAE obtained using the classical technique.)

If you had been given only the Total IBNR of 200, not broken out by IBNER & IBNYR, then the calculation would have been:

unpaid ULAE

= 7.3% x [ 50% x 300 + 100% x 200 ]

= 7.3% x 350

= 25.6

Pop Quiz B!    :-o

• Calculate the unpaid ULAE for CY 2021 using the method from above. Click for Answer 

paid ULAE (CY 2016 - 2020)	30
paid claims (CY 2016 - 2020)	200
inccured claims (CY 2016 - 2020)	280
case2021	500
IBNER2021	100
IBNYR2021	25

Here are 2 exhibits from the Friedland source text that illustrate the classical and Kittel techniques for calculating unpaid ULAE. Take a few minutes to make sure you can follow the calculations.

EXAMPLE:   unpaid ULAE → classical method

EXAMPLE:   unpaid ULAE → Kittel refinement

Kittel Refinement - Concepts

The source text lists key assumptions for the Kittel Refinement but the wording obscures that the only difference versus the classical method is in the stability assumption:

Classical stability assumption: the ratio (paid ULAE) / (paid claims) is stable and reasonably approximates the ratio (ultimate ULAE) / (ultimate claims)

but the Kittel version is:

Kittel stability assumption: the ratio (paid ULAE) / average(paid claims, incurred claims) is stable and reasonably approximates the ratio (ultimates ULAE) / (ultimate claims)

The other 2 assumptions of the classical method (proportionality assumption, allocation assumption) are the same for the Kittel method. The change in the stability assumption is the reason for the change in the formula for the ULAE ratio in the Kittel refinement. Note how Kittel defines incurred claims. This may be useful to know if an exam question doesn't provide the value for incurred claims directly:

CY incurred claims (Kittel)   =   (CY paid claims)   +   (CY change in: total claim liabilities including case and IBNR)

Something worth pointing out is the source text states the assumptions a little differently but it amounts to the same thing. The text says:

• ULAE is sustained as claims are reported even if no claim payments are made
• ULAE payments for a specific calendar year are related to both the reporting and payment of claims

Let's now wrap up this section...

Question: what shortcoming of the classical method does the Kittel refinement address

• Kittel addresses distortions of the classical method when premium volume is changing rapidly

(Kittel ULAE ratio uses incurred claims which are more responsive to changing conditions than paid claims)

Question: what shortcomings of the classical method are not addressed by the Kittel refinement

• 50/50 assumption

(Kittel doesn't allow allocation of ULAE costs between opening, maintaining, and closing claims, which may vary between insurers)

• different rates of inflation between ULAE and claims

(different rates means the Kittel ULAE ratio will never stabilize)

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Practice Problems

Here's a good exam problem on calculating unpaid ULAE. This is one of the few problems where you do have to split IBNR into IBNER and IBNYR, but it isn't difficult. Give it a try. It's from the 2018.Spring TBE exam so there's no PDF but you can check out Alice's well-organized solution below. She solved it using both the classical and Kittel method even though the problem only asked for the classical method. (Once she's had her morning coffee, there's no stopping her.)

Solution: 2018.Spring #23 ← assume the given case, IBNR, and %-case of IBNR pertain to the given AY

And here are some practice problems that will give you a good foundation for the ULAE methods. But remember that once you've done these, you should go over all the old exam problems.

Practice: 4 ULAE problems (like 2018.Spring #23) ← assume the given case, IBNR, and %-case of IBNR pertain to the given AY

Another good exam problem is the following because it illustrates how the 50/50 assumption can be changed. You can check the solution in the examiner's report or against Alice's solution further down.

E (2018.Fall #22)

Note that for part (a), you have to calculate IBNYR but this is not really a ULAE problem. Of course, they are setting you up for the unpaid ULAE calculation in part (b). It's a little unfair because if you don't know how to do part (a) then you can't do part (b) since you need the answer from part (a). What Alice would do in a situation like this is just make up a number (something in line with the given ultimates, but smaller, say between 5,000 & 15,000) and then go on with part (b). Your final answer will be wrong, but if your method is correct you could still get full credit for part (b). That's just one of Alice's world-famous exam hacks!

Practice: 2 ULAE problems WITH 50/50 assumption relaxed (like 2018.Fall #22)

Sorry to do this to you but here's one more. It's a pretty good problem because it combines ULAE with a reserving method from a previous chapter so it's a good review.

Practice: 1 ULAE problem (like 2019.Fall #24)

Here's the Quick-Vid for the web-based problem in the next quiz:

Quick-Vid: F-17 (010) Classical Method ~ 1:00

And finally, here's a selection of more old exam problems:

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Conger and Nolibos Method - Generalized Kittel Approach

This section is 7 pages of confusing formulas that very rarely appear on the exam. Here's what it all boils down to...

Conger and Nolibos is a natural extension of the classical and Kittel methods from above. The classical and Kittel methods had 2 main steps:

• calculating the ULAE ratio
• calculating the unpaid ULAE

It's the same with the CN (Conger & Nolibos). The formulas just look more complicated because we're relaxing the 50/50 assumption and replacing it with 3 separate percentages or ratios U₁, U₂, U₃. The big advantage is that these percentages can better reflect differences between companies in how claims are handled and ULAE is incurred. The downside is that it may not be easy to accurately estimate the values of U_i so parameter risk may increase. It may also be costly. That sort of thing is always a problem when methods become more complicated. Anyway, let's continue...

ULAE RatioCN   =   (paid ULAE)   /   [ U1 x R  +  U2 x P  +  U3 x C ]

where U₁ + U₂ + U₃ = 100%,

U₁ = percent of ultimate ULAE spent opening claims

U₂ = percent of ultimate ULAE spent maintaining claims

U₃ = percent of ultimate ULAE spent closing claims

and

R = ultimate cost of claims reported during time t

P = claims paid during time t

C = ultimate cost of claims closed during time t

For convenience, let W = the ULAE ratio from above, M = the paid ULAE, and let B equal the denominator in the ULAE ratio:

W = ULAE ratio

M = paid ULAE

B = U₁ x R  +  U₂ x P  +  U₃ x C

So W = M/B:

W= M / B

Also, the value of L (see below) would be independently estimated and normally provided separately:

L = total ultimate claims for the same group of AYs used to derive the ULAE ratio W (L is not the same as R)

Then Conger and Nolibos has 3 different formulas for calculating the unpaid ULAE:

unpaid ULAECN   =   W x L – M	EC approach (Expected Claims)
unpaid ULAECN   =   W x (L – B)	BF approach (Bornhuetter-Ferguson)
unpaid ULAECN   =   M x (L/B – 1)	development method approach

This will be much more clear when we look at an example. Despite all these formulas it's a pretty easy method to apply. (Note The selection of the ULAE ratio, W, in the solutions below may not equal the weighted average as stated. The solution is still valid however because judgment can be used to select W. Apologies for the confusion.

Solution: Model Conger-Nolibos Method

Practice: 2 Conger-Nolibos problems (like the model)

And as always you need to know the answer to the following question but it's very easy. You just have to say in words what the U_i percentages are doing within the formulas.

Question: what are the assumptions of the Conger and Nolibos method (Generalized Kittel method)

• ULAE costs are proportional to claim dollars (same as classical and Kittel but different from the Johnson method discussed further down which assumes ULAE costs are propotional to counts)
• ULAE costs spent opening claims are proportional to the ultimate cost of claims being reported (R) - this relates to the U₁ percentage
• ULAE costs spent maintaining claims are proportional to payments made (P) - this relates to the U₂ percentage
• ULAE amounts spent closing claims are proportional to the ultimate cost of claims being closed (C) - this relates to the U₃ percentage

Note that it is the cost of maintaining claims that is not included in the classical or Kittel methods. This can be important for long-tail lines where claims may stay open for many years.

Question: what are the advantages of the Conger and Nolibos method (Generalized Kittel method)

• recognizes ULAE costs for maintaining claims in addition to opening and closing claims (important for long-tail lines)
• relative costs of opening, maintaining, and closing claims can be calibrated to operations of an individual company

Question: what are the disadvantages of the Conger and Nolibos method (Generalized Kittel method)

• doesn't recognize ULAE costs of reopening or reclosing claims
• may be difficult to estimate R (ultimate cost of claims reported during time t) and C (ultimate cost of claims closed during time t)

I'm afraid we're still not done with ULAE. Next we'll look at the Simplified Generalized Approach. I don't think the exam committee considers the rest of the chapter to be very important but they did ask a concept question in (2017.Spring #24) that required a basic understanding. No calculations. As a teaser, I'll tell you that Alice created a fun web-based problem to help you learn some of this stuff.   :-)

Simplified Generalized Kittel Method

Alice and I had a good laugh at the name of this method: Simplified Generalized Kittel Method or SGK. It's funny because the text started with the classical ULAE method, then generalized it to the Kittel method, then generalized it further to the Generalized Kittel Method. Now it feels like we're going backwards by simplifying the generalized method. Please make up your mind! The source text told us that ULAE was a much smaller percentage of total reserves than the loss and ALAE components. Why then are we learning so many different methods for estimating ULAE? I think a full computational question using anything other than the classical method or Kittel refinement is exceedingly unlikely to be asked on the exam. The simplified method discussed below is that last method we're going to go through in detail.

One reason for the simplification is it could be hard to estimate R and C. So instead of R we use a proxy:

• ultimate claims for the accident year (with an adjustment for pure IBNR) instead of ultimate costs of claims reported in the calendar year (R)

And for some lines of business it isn't a problem if we can't estimate C. If closing a claims doesn't require any additional work, we can just set U₃ = 0 in the formula for the claims basis. This is not always a valid assumption however. According to Friedland:

This assumption is not appropriate for all lines of business; for example, professional liability or employment practices liability are lines of business where a significant portion of the claims-related expenses will be incurred with its settlement.

The claims basis B and ULAE ratio W are calculated the same way as before, although you may choose to use the proxy for R when calculating B. The formula for the unpaid ULAE is slightly different however:

unpaid ULAESGK   =   W   x   [ U1 x (pure IBNR)   +   U2 x (L – P) ]

The pure IBNR term in the above formula is the same thing as (L – R). That's the adjustment required to "synch up" the AY ultimate claims with R. It's all very confusing. Poor Ian-the-Intern is tearing his hair out. Next co-op term he is definitely doing a different rotation.

Here's a link to the example from Friedland. Just look it over and absorb it. The mechanics are exactly like the Generalized Kittel Method (Conger and Nolibos) but you set U₃=0 and use AY ultimates instead of RY ultimates in column (3), as noted above. This particular example uses the 60/40 assumption which means U₁=60% and U₂=40%.

EXAMPLE:   unpaid ULAE → Simplified Generalized Kittel Approach

Mango-Allen Refinement

This method is the same as the classical method except for one thing:

Question: how is the Mango-Allen refinement different from the classical ULAE method

• Mango-Allen uses expected CY paid claims instead of actual CY paid claims

(appropriate for a volatile line of business → Ex: low frequency, high severity)

There is a complicated 5-step procedure using industry payment patterns to project CY paid amounts for each AY. They start with an ECR (like in the ECR method from chapter 8), multiply it by the EP to get an expected CY paid amount. But this CY amount must be allocated to development periods for each AY. That's the first page of the exhibit below. The second page simply uses those expected (versus actual) paid amounts in the classical ULAE method.

Interesting observation: In the example below, they show B-values based on both actual and expected paid amounts. The B-values using actual paid amounts are highly volatile and it would be hard make a reasonable selection from these. But the B-values based on expected paid amounts also vary greatly. The difference however is there appears to be a definite downward trend using the expected values. Seeing that pattern may provide more confidence in the final selected ULAE ratio. Still, I would not be overly confident in my final estimated unpaid ULAE for this company.

EXAMPLE:   unpaid ULAE → Mango-Allen refinement

The quiz has a few concept questions on the Conger-Nolibos method and the Mango-Allen refinement.

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Count-Based Methods

The reason for count-based methods (versus dollar-based methods) is that dollar-based methods assume ULAE dollars track with claim dollars in both timing and amount. Alice-the Actuary thinks that's crazy. A claim for $100,000 probably isn't going to result in 20x the ULAE as a claims for $5,000. Not that dollar-based methods are useless – it's just that you need to recognize their limitations and possibly consider alternate methods depending on the circumstances. It's the same reason you have different methods for estimating unpaid loss amounts. The development methods from chapter 7 often work well but if their key assumptions aren't satisfied, you need to use something else.

Anyway, we're going to cover these really quickly. An advantage of all count-based methods is the recognition that ULAE amounts don't always track with claim payment amounts.

Brian Method

assumption: ULAE costs for these 5 claims transactions are similar: opening, maintaining, paying, closing, reopening

method: unpaid ULAE = Σ (historical ratios of ULAE to number of transactions) x (projected number of transactions)

advantage: recognizes that ULAE amounts don't always track with claim payment amounts

disadvantage: requires maintenance work during the year, difficult to estimate number of future transactions

Wendy Johnson Method

assumption: ULAE cost for opening a claim is double the cost of maintaining the claim (considers 2 types of claim transactions)

method: unpaid ULAE = Σ (estimated ULAE per claim activity) x (projected future claim activity)

advantage: allows for different costs for different transactions

disadvantage: requires maintenance work during the year, difficult to estimate number of future transactions

Mango-Allen Claim Staffing Method

assumption: uses a count base called OCP → (Opened claim counts) + (Closed claim counts) + (Pending (ending) open claim counts)

method: unpaid ULAE = (OCP count) / (OCP count per adjuster) x (trended ULAE cost per adjuster)

advantage: required information can be derived from a typical reserve study

disadvantage: sensitive to selected parameters

Rahardjo Method

assumption: ULAE dollars vary with the length of time a claim has been open

method: incorporates the relationship between ULAE costs and claim duration

advantage: applicable to TPAs (Third Party Administrators for claims handling) which are often used by self-insured entities

disadvantage: relationship between ULAE dollars and claim duration may be difficult to estimate

Spalla Method

assumption: computer can track time spent on individual claims by individual employees

method: unpaid ULAE = Σ (time spent by employee) x (cost of employee per unit time)

advantage: leverages modern computing resources

disadvantage: large up-front costs to setting up such a sophisticated system (plus it might make the workplace feel like a surveillance state)

Conger and Nobilos Method applied to counts

The assumptions, method, advantages, and disadvantages are essentially the same as for Conger-Nolibos dollar-based method. The only difference is you use count data instead of dollar-based loss data.

Triangle-Based Methods

One of the first things we learned is that you cannot make triangles for ULAE. That follows from the definition of unallocated – you cannot allocate ULAE payments to an accident year and development period which means you cannot make a triangle. What then is going on here? Well, actuaries did come up with a few different methods for allocating ULAE payments to cells in a development triangle.The source text very briefly mentions 3 ways this can be done but provides no full examples and notes that actuaries rarely use triangles to estimate ULAE. For that reason, we're not going to spend much time here. Here are Alice's 1-phrase summaries of each of the 3 methods:

• allocate CY ULAE payments to a triangle based on claim payment patterns
• allocate CY ULAE payments using a time & motion study that measures resource allocation between current & prior AYs (Slifka method)
• allocate CY ULAE payments using a time & motion study with both reported & paid claim development patterns

It's nice to have a triangle because we already have so many triangle-based methods but the devil is in the details. These triangle-based ULAE methods depend on how accurately you've allocated the ULAE payments to the triangles in the first place. It seems very contrived and Alice has never done her ULAE estimates this way.

In the next quiz, there's a web-based problem to help you review the ULAE methods discussed in this chapter. Here's the Quick-Vid for it...

Quick-Vid: F-17 (050) ULAE Methods ~ 1:00

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Pop Quiz A - Answer

Classical method:

ULAE ratio = 30/200 = 15%

unpaid ULAE = 15% x [ 50% x (500 + 100) + 100% x (25) ] = 48.8

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Pop Quiz B - Answer

Kittel refinement:

ULAE ratio = 30/average(200,280) = 30/240 = 12.5%

unpaid ULAE = 12.5% x [ 50% x (500 + 100) + 100% x (25) ] = 40.6

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