Splines in Emblem

[Entact30]

I saw recently in Emblem there is an option to include "Splines" in a curve. To be perfectly honest, this was the first time I came across the idea and I was hoping there might be some useful information on this forum about Splines - Splines are not included in any of the UK actuarial exams!

I have looked through some of the threads but they all refer to the actuarial exam which exams the subject. I would be very grateful if someone could give a high level explanation the following:

1) What are splines (from a GI actuarial modelling context) - from the material I have read they appear to be a way of fitting a curve that passes through a point rather than around it. By doing this you are really combining two or more different curves - I am probably completely off in my interpretation.

2) Why would an actuarial modeller need to use splines - what are the advantages? They seem to increase the danger of overfitting? Yes, the actual and fitted will be closer but increase in predictive power will be questionable.

Many thanks in advance

 

[Calum]

Roughly speaking, a spline curve is a set of curves which join on to each other to produce a single, more complex curve. Each individual curve is a simple analytic function, often quadratic or cubic and each joins onto the next at the same point with same first and second derivative.

The advantage is, in short, you can model complex curves using fairly simple functions and model them to an arbitrary level of complexity. Overfitting is not, I think, such an issue as you are just drawing a curve between points you've already derived - effectively the overfitting occurs in the prior step.

One common actuarial application, albeit not GI, is in mortality - force of mortality \(\mu\) can be modelled as a spline curve and this approach seems to be becoing quite popular.

This seems like a reasonable introduction to the theory:

http://www.ae.metu.edu.tr/~ae464/splines.pdf

 

[Entact30]

Thanks Calum, that's very helpful

Do you know if it is used much in GI? I assume it is if it's an option in Emblem.

 

[td290]

Put simply, splines are a very flexible class of curve, much more flexible than straight lines or quadratics for example. You might use them if you had to fit a curve to an awkward shape that a simpler class of curve wouldn't capture very well. Of course, because the curve is more flexible, overfitting is a danger. It's your job as the modeller to decide whether the advantages outweigh the disadvantages in any given situation. No idea what the rest of the market is doing - they will all have their own approaches for their own reasons.