Clark Question

[TwoStep]

Why when the ELR for the Cape Cod method is calculated, does Clark use un-truncated %Paid values, but then when the reserve is set, he uses the truncated paid values? Are we not over estimating the loss ratio because the used premium is under estimated (because we think, based on not truncating, that less % of the total losses have emerged)?

Thoughts? Am I reading the Clark paper wrong?

[Shouxiaozi]

My understanding is the truncation only relates to the fact that we are extrapolating the loss emergence by the curve, either Loglogistic or Weibull as presented by Clark. If you choose Loglogistic, truncating may be needed depending on the LOB since Loglogistic tend to have heavier tail. Clark did mention that an alternative to using Loglogistic and then truncating is to use a curve with lighter tail like Weibull.

[TwoStep]

My understanding is the truncation only relates to the fact that we are extrapolating the loss emergence by the curve, either Loglogistic or Weibull as presented by Clark. If you choose Loglogistic, truncating may be needed depending on the LOB since Loglogistic tend to have heavier tail. Clark did mention that an alternative to using Loglogistic and then truncating is to use a curve with lighter tail like Weibull.

I understand, but why not truncate before calculating the ELR? Isnt this over estimating the ELR?

[doop]

I understand, but why not truncate before calculating the ELR? Isnt this over estimating the ELR?

That's actually a great point, my guess is they just overlooked that fact?

[TwoStep]

You know, the TIA instructor seemed confused about this too. Rather than argue a point on the exam though, I would rather just do it the way to paper does it and not wake any sleeping dogs.

[Joshua0317]

Re-visiting Clark, and while looking for an answer to a different question I came across this question. Here is my take on it:

You can't truncate the estimation of a parameter that is based on parameters you have yet to estimate. You are using all of your data points to estimate theta and omega, which will define your estimated curve for your emergence. You are using these parameters to estimate ELR. In addition, the derivative of the curve form required to estimate in log-likelihood is going to be hard to do when you have a piecwise model. It is much more practical to estimate your parameters with log likelihood, find an issue with the tail, and then handle it then it is to complicate your curve form and estimation.

One thing this made me realize is, although Clark breezes on through, we need to use log-liklihood to get the parameters of the curve. Sure the ELR is nice and easy and works out to Cape Cod, but don't forget that you also need to set the first derivative of the rest of the parameters equal to zero and solve as well. It is my belief that this elaboration was left out since most stat packages will just do it for you, and the inclusion of the Ult/ELR was only to prove its similarity to the current methods.