Fun with random effects in loss reserving

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For some time now, I’ve advocated for the view that non-life loss reserving constitutes a categorized linear regression. I’ll emphasize that the idea of a linear regression isn’t remotely novel. Further, the categorization is the de facto approach. I’m merely recognizing it and suggesting instances where a decision may be made about the optimality of the categorization.

Anyway. I prepared some data to have a bit of fun with. This is taken from the NAIC data set hosted on the CAS website. I’ve combined the results of several different lines for the 27 companies which had results for those lines. The code to construct that dataset may be found in this Gist. Once that’s done, I can look at how incremental paid varies, presuming that the development age constitutes the random effects.

dotplot(reorder(DevInteger, IncrementalPaid) ~ IncrementalPaid, df,
        ylab = "Development Lag", jitter.y = TRUE, pch = 21,
        xlab = "Incremental paid",
        type = c("p", "a"))

That produces this lovely picture:
RandomEffectsIncrementalPaid

Now the fun stuff. How does incremental paid loss vary by line of business and company?
IncrementalPaidByCompany
No surprise that some companies have a great deal more variance than others. For those in the bottom half of the chart, one could probably increase predictive power by combining data across companies.

IncrementalPaidByLine

The small variation and low mean for GL is quite surprising. For the others, the consistency in scale and variance, suggests that it may make sense to combine these lines. I’ll delve into that in a subsequent post.

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