Friedland16.ALAE

Chapter 16: Estimating ALAE (Allocated Claim Adjustment Expenses)

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

BattleTable

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

• multiplicative method - a ratio method for calculating ultimate ALAE
• additive method - a ratio method for calculating ultimate ALAE
• advantage/disadvantage - of ALAE ratio methods
• ALAE ratio methods - additive versus multiplicative method

reference	part (a)	part (b)	part (c)	part (d)
E (2019.Spring #24)	multiplicative method: - ultimate	ALAE ratio methods: - additive vs multiplicative	advantage/disadvantage: - of ALAE ratio methods
E (2018.Spring #25)	paid ALAE development: - ultimate	additive method: - ultimate	justify final selection: - ultimate
E (2017.Spring #25)	paid ALAE development: - ultimate (with large loss)	multiplicative method: - ultimate (with large loss)
E (2016.Spring #23)	additive or multiplicative: - ultimate	advantage/disadvantage: - of ALAE ratio methods
E (2015.Fall #24)	multiplicative method: - ultimate	additive method: - ultimate	justify final selection: - ultimate
E (2014.Spring #21)	paid ALAE development: - challenges	ALAE ratio methods: - challenges	frequency-severity: - for legal expenses

In Plain English!

Let take a quick look at a very simple concept. Suppose you have a development triangle as follows:

AY	12	24	36
2018	15	20	22
2019	16	21
2020	15

The standard way of calculating link ratios is to form the quotient of a given value with the value in the previous column. This is multiplicative development:

AY	12-24	24-36
2018	1.33	1.10
2019	1.31
2020

But another way of calculating link ratios is to form the difference of those same values. This is additive development:

AY	12-24	24-36
2018	5.0	2.0
2019	6.0
2020

The multiplicative method is commonly used for estimating ultimate claims when we're given a paid claim or reported claim triangle. We call that paid loss development and reported loss development. The additive method works exactly the same way except wherever you would multiply or divide, you now add or subtract.

The additive method would be terrible for developing claim amounts however! The reason is that it doesn't take into account differences in claim volume between accident years. But if you apply the additive method to ratios rather than directly to amounts, then it often works pretty well. In fact the ratio methods, either multiplicative or additive, are the most common methods for estimating ultimate ALAE.

Question: identify 2 common methods used to estimate ultimate ALAE

• development of paid ALAE triangle to ultimate in the standard way

(this method has issues because ALAE data is often thin compared to claims data)

• ratio methods: uses triangle of (paid ALAE $s) / (paid claim $s)

   - may be developed multiplicatively (as in the standard development method)

   - may be developed additively (link ratios are calculated as a difference instead of a quotient)

You can see from the BattleTable that this is question you need to be able to answer:

Question: describe advantages & disadvantages of using ratio methods to estimate ultimate ALAE

advantages of ratio methods:

• ratios recognize the relationship between loss & ALAE
• ratios provide diagnostics (individual AYs can be excluded if unreasonable)
• ratios are more stable than developing ALAE directly (ALAE can be small & highly leveraged, especially at early maturities)

disadvantages of ratio methods:

• inaccurate ultimate loss estimates may cause inaccurate ALAE estimates
• timing of ALAE payments may differ from timing of loss payments (causes distortions in ratio triangle)
• trend for ALAE payments may differ from trend for loss payments