I think it needs another serious revamp. There seems to be an unusual mix of relevant, technical/ and useful material with some unrelated shallow chapters which just do not blend with the other major topics. I particularly enjoyed the chapters on Bayesian methods loss distributions and credibility, these seem to flow well. Also the chapters on Time series and Risk models are very well set out and are packed with useful information. However it’s a shame that the subject contains these stand alone, useless chapters which do not fit with the theme of the subject such as, 1. Decision theory, which would be more suited to a 1st year course in microeconomics or operations research. 2. The chapter on Monte Carlo methods would be more fitting in CT3 3. The chapter on run off triangles does not make use of any statistical theory whatsoever 4. The chapter on reinsurance which is more a review of basic integration techniques 5. The chapter on generalised linear models which is really only the most basic of introductions to the topic and is not covered in any serious depth. Any thoughts or other opinions on this? I’d be particularly interested to hear what John has to say about the subject in general.
I have to agree (mostly)... 1. I undersatnd why its in there. It's a way of intorudcing prior distributions, but probably not worth the space. 2. Not sure I agree on this. It makes most sense with the time series stuff. 3.Yeah! What a load of rubbish. 4. If we assume people actually know their ct3, then this could be condensed. 5.There is absolutely zero chance that you could implement a GLM using CT6. Very sad, as I imagine it is the cornerstone of pricing GI (I work in life so wouldn't know)
With regard to 5: I have studied GLMs in a little more depth than the course. In my opinion, the CT6 course covers the minimum essential theory of glms and it would be difficult to extend this without introducing a lot of extra material. One way of extending the course would be to cover normal models in greater depth, and the links between the analysis of normal models and of glms. In fact, gaining practical experience of data analysis, e.g. using R for linear regression and tests of means, might be more valuable. Having learnt to do this, it would not then be difficult to implement a glm with R, but the difficulty is with drawing valid conclusions that can be justified. There is a lot of theory involved in a full glm data analysis, e.g. sampling distributions of score statistics, MLEs and deviances, quadratic forms, orthogonal parameters, binary variables (logistic regression) and count data (Poisson regression). A key result that is a challenge to understand is for the normal linear regression model y = Xβ + e. The MLE of β is given by β = (X'X)^(-1)X'y, where E(Y(i)) = x(i)'β, Y(i) ~ N(μ(i),σ^2), y is the data vector, β is the vector of parameters for the model and e is the vector of residuals. X is the design matrix of the parameters (composed of the x(i)') and X' is the transpose of X. I would suggest Linear Models with R, and Extending the Linear Model with R (covers glms and other models) by Julian J. Faraway as being useful books to read on this topic initially, and also An introduction to generalized linear models by Annette J. Dobson. Some additional knowledge of matrices may also be needed.
Well with an invitation like that - how can I resist? Fair point - but it's nice to have an easy question on CT6 (especially after the departure of no claims discount systems)!!! There is some overlap - as inverse transform is covered there. It's usefulness here is because of the time series modelling and ruin. We model e(t) as normal RVS and simulate them and therefore can not only use k-step ahead to get the mean value of the tfuture time series but also get the range of values. In ruin - typically this would be calcualted using simulations - the connection is not made very well - as the sources of the chapters are different. Couple of points: This is a general insurance exam and this is one of the few areas that every GI in the tutorial goes "I use this at work". There is the statistical model that underlies the techniques given - but admittedly not much use is made of it explicitly. However, what isn't made clear is that the BF method is actually a credbility weighting of the loss ratio and the development factors (and can be derived more easily from them). Hence a useful extension of the Ch5 material into GI work. It's a shame that this is not made clear - as this is a very good reserving application (rather than a pricing application). True - but it is an important application in GI work. True - however, there's no point spending hours on the theory as we can't do much with it on a piece of paper - and the exams are more application based rather than theoretical (read: boring proofs) based. The reality in GI is that we just use the program/excel macros to do it - so need only an understanding of what's going on behind the scenes and how to interpret the results. Don't know if that helps quell the rage or not?!
