XS LDFs - curve fitting

[The Mantastic Actuary]

When creating excess LDFs, is there a specific curve that anyone feels fits the data better than other curves?

Specifically, when using ResQ, I am given the option between exponential, inverse power, power, and weibull. We generally use the inverse power curve since it is the default. However my boss was wondering if we have a reason for that (other than it is the default and that was the curve of choice prior to me starting at the company)?

So if anyone can help validate the choice or give me any reasons why another curve would be better it would be helpful.

Thanks

[Avi]

IIRC, the power curves have a thicker tail than the exponential and the weibull, so that would make more sense if you are trying to extrapolate above your dataset in excess layers.

[The Mantastic Actuary]

IIRC, the power curves have a thicker tail than the exponential and the weibull, so that would make more sense if you are trying to extrapolate above your dataset in excess layers.

but do we necessarly want a thicker tale in excess lines of WC/GL/AL? This is my first time doing XS LDFs so any outside views would help

[Avi]

IIRC, the power curves have a thicker tail than the exponential and the weibull, so that would make more sense if you are trying to extrapolate above your dataset in excess layers.

but do we necessarly want a thicker tale in excess lines of WC/GL/AL? This is my first time doing XS LDFs so any outside views would help

From my, admittedly limited (4.5 years) experience, the tails in WC and GL (especially Prods/CO) are not thick enough. Maybe someone who works at NCCI or ISO can shed more light on the matter, but I somehow recall that at one point exponentials were used, and power curves were selected afterwards as a better fit to the data because of their thicker tails.

I think it is safe to say (and one of the beauty's of this board is that if I am wrong, someone will gleefully come and skewer, cough, I mean correct me) that since loss distributions, especially long-tailed ones, and doubly-so in excess layers (where leveraging takes on sometimes truly horrific proportions), are highly skewed, the mean is so much greater than the mode, that there really is not enough data to fit extreme events, and any fit will be biased low in the tail; thus the desire for a thicker tail, within reason. The higher up you go (e.g. 5Mx5M vs. 250K vs. 250K), the less credible the data and the more likely one extreme event will dominate the results.

[The Mantastic Actuary]

the argument makes sense to me. Do you know where I'd be able to find the article that talks of the transition from using exponential to power or inverse power functions?

[Avi]

I do not remember if that actually occurred :oops: but here are some sources for your perusal:

http://www.casact.org/education/clrs/2004/handouts/miller.doc (Page 21)

http://www.actuaries.org.uk/files/pdf/giro2002/Lyons.pdf (Specifically 84-99)

Of course, Sherman's paper on the inverse power curve: Extrapolating, Smoothing and Interpolating Development Factors (http://www.casact.org/pubs/proceed/proceed84/84122.pdf)

Hope that helps

[The Mantastic Actuary]

Thanks... this helps lots :tup:

[Third Eye]

I would also advise doing some sensitivity testing. If you have time, try the analysis with different assumptions to see how much difference it makes.

The most important thing here is humility - we know very little about your actual excess curves, because there's not much data, and your superiors are not giving you guidance. ISO has some information on excess LDFs available to reinsurers (as well as their Increased Limit Factors), but it's not cheap, and it might not apply to your book of business. I agree with Avi that the exponential tail is probably not thick enough, but beyond that it's likely to be a matter of judgment - another element of judgment in reserving.

[The Mantastic Actuary]

agreed.... the articles that Avi found were extremely helpful. Inverse power is pretty much the standard we use. The chief actuary of my department had a question regarding why we use it. So the articles (especially the Lyons one) worked nicely to answer the question.