Archive | December, 2012

Empirical Bayes Credibility

6 Dec

The chapter on Empirical Bayes Credibility is one of the most criticised, if other blogs and forums are anything to go by. The usual criticism is that the treatment makes the this subject more confusing than it really is.
The chapter implements an approach to credibility theory that doesn’t require any assumptions about the prior distribution – a non-parametric approach. Given that fitting a distribution makes our life easier on the maths front, and allows for a more precise estimate, it is important to remember that on the con side it is difficult – particularly in the absence of a large data set – to show that our data follows a particular distribution. A better way and more correct way of expressing the preceeding idea is that there is a real danger of overfitting if we assume a particular distribution.

There are two models outlined. CT6 core reading calls them model 1 and model 2. Model 1 is the simplest available implementation of this method, and the core reading says that it more useful for learning than for doing. This model is known outside the world as Buhlmann credibility. Model 2 has the added complication of making adjustements for the volume of business in each year.

Given that people find it difficult to use the CMP for this material, it is worth remembering that we are not stuck with using that material to learn this stuff. Apart from Loss Distributions, which runs the material quickly, there are a number of sets of lecture notes available online which cover the same material.

Of these, one of my favourites is

http://www.math.ku.dk/~schmidli/rt.pdf

This treatment discusses both the derivation of the two methods and gives examples of how they are used. An alternative more concise version can be found here:

http://personalpages.manchester.ac.uk/staff/ronnie.loeffen/risktheory2013/risktheory_2013_main.pdf

The final resource I suggest is the ‘study note’ on credibility theory supplied by the SOA/CAS which is actually a draft chapter from Foundations of Casualty Actuary Science. It can be found here :

Foundations of actuarial science

For a reader in the Institute of Actuaries system there are pros and cons to this resource. The con side is that the notation is different to the notation used by the CT6 Core reading. On the┬ápro side, there are plenty of examples and exercises, and, I think importantly, examples and exercises which strip out the purely actuarial/ insurance from a quintessential problem facing anyone working with data from more than source (be it experiment, survey etc) – how can these multiple data sources be used together to form a more accurate view of the object of interest?