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	ultimate claims	ultimate claims ratio
2017	1,000	750	75%
2018	1,000	750	75%
2019	1,000	750	75%
2020	1,000	750	75%
2021	1,000	?	ECR = 75%

Projecting an ECR of 75% for AY 2021 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 given the following:

annual loss trend = 2%

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

AY	OLEP	ultimate losses	trend factor	trended ultimate losses	ultimate losses ratio
2017	1,000	750	1.024		75%
2018	1,000	750	1.023	75%
2019	1,000	750	1.022	75%
2020	1,000	750	1.021	75%
2021	1,000	?	ECR = 75%