On tail estimation in triangle-based reserving

The main idea: applying autoregression of development factors to estimate the tail.

0. Posts on this blog are ranked in decreasing order of likeability to myself. This entry was originally posted on 06.10.2021, and the current version may have been updated several times from its original form.


1.1 This technique would be incredibly obvious to anyone who has reserved non-life by triangles, and the only reason I’m posting of it is that I have not encountered it anywhere. Haven’t looked too hard though.

1.2 So you set up your reserving triangle, which you hope to complete by chain-ladder but - oh no! – development does not appear to be over (even if it does appear to be, is it really?).


1.3 What do you do about that tail, replicate the last factor, replicate its square, double, what? Well, first of all cumulate your development factors.

1.4 Now the next step is obvious. Just set up a simple autoregressive model on the cumulated factors, predicting each based on the factor preceding it.

1.5 If you are in luck, your slope will be between zero and one, which allows the autoregression to tell you that this model will reach a limit of Intercept / (1 – Slope). Divide this by your last cumulative development factor and there goes you tail.




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