Friedland11.FreqSev

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

Chapter 11: Frequency-Severity Methods

BattleTable

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

• fact A...
• disposal rate method - calculate ultimate/unpaid amounts with trending and adjustments for court decisions

reference	part (a)	part (b)	part (c)	part (d)
E (2019.Fall #20)	disposal rate method: - unpaid	Freq/Sev vs Paid Devlpt: - why Freq/Sev better
E (2019.Spring #15)	unpaid claims: - freq-sev method	identify scenario: - rptd claims down
E (2019.Spring #20)	tail severity: - provide an estimate	tail severity: - selection of maturity age
E (2018.Spring #18)
E (2017.Fall #18)	ultimate: - Freq-Sev method	trend in counts: - explain	seasonality: - suggest diagnostic
E (2017.Fall #20)	ultimate frequency: - select & justify	ultimate severity: - select & justify	ultimate: - B-F & Freq-Sev methods
E (2017.Fall #23)	tail severity: - provide an estimate	tail severity: - selection of maturity age
E (2017.Spring #16)	IBNR: - Freq-Sev method	ads/disads: - Freq-Sev method
E (2017.Spring #17)	ultimate: - Freq-Sev method
E (2016.Fall #20)	disposal rates - good: - Freq-Sev method	disposal rates - not good: - Freq-Sev method	adjustments: - to Freq-Sev method
E (2016.Fall #22)	settlement rate change: - provide evidence	ultimate: - Freq-Sev method
E (2016.Spring #19)	does Freq-Sev work?: - long-tailed lines	does Freq-Sev work?: - many reopened claims	does Freq-Sev work?: - spike in high-severity clms	does Freq-Sev work?: - change in case reserving
E (2015.Fall #20)	does Freq-Sev work?: - general liability	does Freq-Sev work?: - reduced deductibles	unpaid claim estimate: - suggest improvement
E (2015.Spring #20)	ultimate: - use several methods	do methods work: - discuss
E (2015.Spring #21)	disposal rate method: - ultimate	disposal rate method: - adjust for severity spike
E (2014.Fall #16)	estimate of counts: - assess reasonableness
E (2014.Fall #17)	disposal rate method: - unpaid	legislative reform: - assess impact
E (2014.Spring #16)	ultimate counts: - reins. attachment points
E (2013.Fall #16)	IBNR: - Freq-Sev method
E (2013.Spring #19)	IBNR: - Freq-Sev method

In Plain English!

Example A: Intro to FS Methods

Alice likes to use "FS" as an abbreviation for Frequency-Severity so we'll follow her lead. The concept behind FS methods is super-simple. Recall:

frequency = counts /exposures

severity = losses / counts

I'm going to use the term "losses" in this chapter, not "claims". (The reason is that it's too easy to get "claims" confused with "counts") So, we'll refer to losses and counts. Recall also that in practice paid counts usually means the same thing as closed counts. That ignores the possibility of partial payments where a claim could be paid but not technically closed, but let's agree for our purposes here that paid & closed mean the same thing.

The simplest possible example of the FS method is this:

• ultimate counts for AY 2025 = 100
• ultimate severity for AY 2025 = $2,000

Then,

• ultimate loss for AY 2025 = 100 x $2,000 = $200,000.

This is because if you multiply the counts by the severity, the counts cancel out and the result is losses.

Example B: FS Methods - Developing Counts and Severities

Let's build on the idea from the previous section.