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Old 11-16-2019, 12:05 PM
TDH TDH is offline
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Default severity trends - IBNER adjustments?

I am trying to figure out how to calculate an IBNER (incurred but not enough reported) adjustment. I have googled and have come with two approaches:

Method 1. Create a triangle grouped by reporting year and look at the incurred amounts by each development period. Use the usual CL techniques to get the LDFs and eventually a pattern that can be used to the data. You can then adjust every claim amount by looking up when the reporting year of the claim (i.e. the year at which the claim first became >0) against your selected development pattern and use that factor to adjust the severity up to ultimate.

As you are using reporting year, you are sure that you are not getting "new" claims as you go across the development period (i.e. pure IBNR is excluded). The downside of this method is that you need to have the reporting year of the claim and your triangle cohort will have to be reporting year.

Is this method correct? As you are including both open and closed claims in the triangle, is it right to project claims that are closed?

E.g. say you had a claim with a loss year of 2015 and reported year of 2017. Your selection said that claims with a report year of 2017 are 50% developed. When projecting each claim, this method would take the current claim amount and divide by 0.5, regardless if that claim is open or closed.

Method 2. I found this method by googling in a book called "Pricing in General Insurance". They have an example spreadsheet: http://www.pricingingeneralinsurance.com/home/downloads

Looking at: Chapter 15: IBNER adjustment.

The method is different from the first. IT seems to not create a triangle at all and instead look the OS % (OS / Incurred). When calculating the factor it only includes claims where the OS% is >0 in the prior development period.

What I don't understand about this method is what "period" is being referred to in the tab "OutputIBNER factors - output". If I wanted to apply the development factors to individual claims, would I be doing it by loss year or reporting year or policy year or does it not matter at all in this method? Do I use the factors for both open and closed claims? I am assuming we can group the claims by any reporting/policy/accident year as we are automatically excluding pure IBNR by ensuring the prior year has an OS % >0?

In general, I'm trying to understand what the standard approach is here. The endgame is to get some IBNER factors using the standard triangulation methods and apply them to individual claims for use in a frequency/severity model.
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Old 11-25-2019, 05:20 PM
r8ingStuff r8ingStuff is offline
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One idea is instead to adjust your LDFs to be used on open claims only. I stole this idea from the paper "The 2004 NCCI Excess Loss Factors" - Section 2 (Individual Claim Development).

if L_c = Aggregate undeveloped loss for closed claims
L_o = Aggregate undeveloped loss for open claims
lamda = Aggregate LDF applicable to all claims
lamda_hat = Open only LDF

then,

lamda * (L_c + L_o) = L_c + (lamda_hat)*L_o ==> lamda_hat = lamda + (lamda - 1)*(L_c / L_o)
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