Greetings fellow Actuaries:
I am looking to learn about methods for estimating ILFs from empirical data. Any suggestions are appreciated.
I’d divide it into two pieces so you’ve got credible losses up to some limit that you fully use your empirical data for and then you get more creative with the higher limits, where more creative is something like credibility weighting your empirical ILF against ISO or fitting a curve or some combination of those.
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This. Your data will only be credible up to some point, and then you’ll have to get creative for everything above.
Each LOB acts differently; there is no “one ILF curve fits all” approach. [Because you’re only looking at one LOB here, right? You won’t believe how many times I’ve seen someone try to combine LOBs and look at development or ILFs assuming all LOBs behave the same.]
You only want to look at ground-up losses. If you have large deductibles in the data, you’ll want to exclude them completely. Same thing for retros.
but now I’m credible!
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The Exam 5 ratemaking manual will give the basics on using empirical data to estimating ILFs, with some additional references for more detail. The Exam 8 Distributions monograph goes into some of the curve fitting procedures and the assumptions and properties expected of ILFs. ISO also publishes their methodology on how they create their ILFs for various lines.
If your losses are censored by policy limits or truncated by deductibles, you can still fit a curve with additional assumptions.
Treatment of trend and development is more complicated. The easy way is to adjust your data for trend and only use completed losses. On the other end you can build a full-blown Bayesian model of the loss distributions but this is still uncommon today and likely to be overkill.