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: - expected claims method	Friedland09.BornFerg
E (2016.Spring #16)	unpaid claims: - expected claims method	Friedland07.Development	Friedland09.BornFerg
E (2015.Fall #17)	Friedland07.Development	ultimate claims: - expected claims method
E (2015.Spring #18)	ultimate claims: - expected claims method
E (2014.Fall #15)	IBNR: - expected claims method
E (2014.Spring #19)	ultimate claims: - expected claims method

In Plain English!

Example A: Very Easy

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.

Example B: Estimating ECR

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 a column into the table above for the trended ultimate losses.