Friedland08.ExpectedClms

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

Chapter 8: Expected Claims Method

BattleTable

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

• fact A...
• fact B...

reference	part (a)	part (b)	part (c)	part (d)
E (2017.Spring #18)	unpaid & IBNR: - ECR method	Friedland09.BornFerg
E (2016.Spring #16)	unpaid claims: - ECR method	Friedland07.Development	Friedland09.BornFerg
E (2015.Fall #17)	Friedland07.Development	ultimate claims: - ECR method with trend
E (2015.Spring #18)	ultimate claims: - ECR method with trend
E (2014.Fall #15)	IBNR: - ECR method with trend
E (2014.Spring #19)	ultimate claims: - ECR method with trend

In Plain English!

Example A: Intro to ECR Method

Recall that LR normally stands for Loss Ratio, and that this is the same things as CR or Claims Ratio. Let ECR stand for Expected Claims Ratio (this is an ultimate value) ECR is a projection, or an expectation of what the loss ratio or claims ratio is going to be in a future period. Let's start with a very simple example of the ECR method. Suppose you're given:

ECR = 75% (based on historical CRs from the past few years which were all 75%)

EP = 1,000

Then by the ECR method:

ultimate claims   =   ECR x EP   =   75% x 1,000   =   750

To say this in words, if you think the ultimate claims ratio for a particular year is going to be 75%, and you also know the EP is 1,000, then the ultimate claims (in dollars) is obviously just the product of ECR and EP. Let's extend this example a little bit by supposing you also know:

paid loss = 600

reported loss = 850

Then using Alice's Pro Tip & Mega-Useful Formulas we can calculate the following:

IBNR = (ultimate loss) – (reported loss) = 1,000 – 850 = 150

case O/S = (reported loss) – (paid loss) = 850 – 600 = 250

Then it's an easy matter to get:

total unpaid = (case O/S) + (IBNR) = 250 + 150 = 400

This is all you need to know to do part (a) of these 2 exam problems. Give them a try now. They should only take a few minutes each.

E (2017.Spring #18)

E (2016.Spring #16)

The above 2 exam problems are also included in the quiz so you can keep track of how you did on them and also when you last did them.

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Example B: Estimating ECR using Loss Trends

In the previous example the actuary came up with an estimate of 75% for the ECR just by looking at past years and assumed nothing would change going forward. The data may have looked something like this:

AY	OLEP 1	ultimate claims	ultimate claims ratio
2020	1,000	750	75%
2021	1,000	750	75%
2022	1,000	750	75%
2023	1,000	750	75%
2024	1,000	750	75%
2025	--	--	ECR = 75%

¹ OLEP = On-Level Earned Premium. This is a pricing concept where the EPs used in calculating a rate change are brought to current level by adjusting prior years' premiums using rate change information over the intervening period.

Based on the above talbe, projecting an ECR of 75% for AY 2025 looks reasonable, but estimating the ECR is the key to this method so let's see if we can be a little more sophisticated. Suppose you're also told:

annual loss trend = 2%

Then we can insert 2 columns into the table for the trend factor and trended ultimate claims.

AY	OLEP	ultimate claims	trend factor 2	trended ultimate claims 3	trended ultimate claims ratio
2020	1,000	750	1.025	828	82.8%
2021	1,000	750	1.024	812	81.2%
2022	1,000	750	1.023	796	79.6%
2023	1,000	750	1.022	783	78.0%
2024	1,000	750	1.021	765	76.5%
2025	--	--	--	--	ECR = 79.6%

² Assume claims (losses) are trended from mid-year to mid-year so trend exponentes are integers.

³ trended ultimate claims = (ultimate claims) x (trend factor).

I selected the ECR to be the average of prior years. Actually this probably isn't the greatest example because it looks like there's a downward trend in ultimate loss ratios. That means it would also be reasonable to select 75% for the ECR, which is what we had in the first place without the trending! But you get the point: In general, losses should be trended to their current level to get a more accurate ECR estimate. Then the final ECR selection is a matter of judgment.

Further down is a link to a pretty straightforward exam problem using the ECR method with a claim trend. But there is a small catch: You are not given ultimate claim amounts for any year. You have to calculate them yourself in part (a) of the problem using the reported development method. Alice has some advice for you...

Alice's ECR Tip #1: To get the ECR method "started", you need ultimate claim estimates from some other method, often the paid or reported development method.

Comment: If the paid and reported development methods are stable and give you good answers then you really don't need the ECR method. But if you're unsure about the accuracy of the development methods (maybe the paid and reported methods produce widely varying estimates for no discernible reason) you can instead use them as a starting point to come up with a judgmentally selected ECR.

Alice's ECR Tip #2: If you want to use the ECR for a particular AY, make sure to exclude the initial ultimate claim amounts for that year when coming up with your ECR

Comment: If you are asked to estimate the ultimate for AY 2025 and you have initial claims estimates for AY 2020 to AY 2025 from the development method, do not include the initial estimate for AY 2025 when coming up with your ECR. Make sure to read the examiner's comments for the problem below as points were deducted for not following Alice's ECR Tip #2.

Ok, here's the problem:

E (2015.Fall #17)

This next exam problem is very similar except instead of Expected Claims Ratio, you use Pure Premium. Pure premium is covered in the pricing section and the formula is as given below:

Pure Premium = claims / EE

Comment: EE = Earned Exposures is an exposure base kind of like Earned Premiums. It's a measure of the level of risk. For example in auto insurance, we can use Earned Car-Years as an exposure base. If 1 person has a policy valid for 1 year, then over the course a year EE = 1. In the problem below, the exposure base is occupied hospital beds so the formula for pure premium (or ECR) in this case is (claims)/(occupied hospital beds).

So, give it a try. There are no other tricks.

E (2015.Spring #18)

The above exam problem is also included in the quiz.

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