 Welcome back to the GI Insight column. If you are new to this column, we are part way through having a look at how insurers take decisions in a (very) uncertain world. We also introduced an example based on the insurance of fleets of motor vehicles.
This month we will look at how to deal with the uncertainty of setting a premium, given the different claims experiences of different fleets. We will see why poor experiences no longer need to lead to knee jerk reactions. This will then lead us to next months’ column where we will talk about farming (can you guess why?) and then we will finally stand back and ask whether we are really deluding ourselves and missing seeing the bigger picture (which is probably the perfect point to take a summer holiday!).
I need to introduce the topic of “credibility theory”. I am afraid though that in so doing, you are going to label me as a “Pure Actuary”. This follows my reading of a (reasonably) funny paper by Matthew Rodermund on the three types of actuaries. To give some idea of his paper, I quote the following paragraph: “A discussion of an actuarial problem that includes the word "stochastic" is a discussion by a pure actuary. A discussion in which the favourite descriptive term is "fantastic" is probably a discussion by a lay actuary.” You get the idea.
I was frightened further when reading a credibility theory book on the tube the other evening, the person next to me started speaking. As you know, this itself is a rare event (and could be stochastically modelled). He said, “Excuse me. I hope you don’t mind me saying that what you are reading is the most complicated thing I have ever seen anybody read on the tube”. I was actually lost for words. (If you have any ideas as to what I should have said – please forward them to me at my email address below – at least I will know what to say if I ever do dare to read Klugman, Panjer and Willmot on the tube again.)
Anyway back to credibility. We will use the example from Stephen Philbrick’s paper (definitely a Pure Actuary masquerading as a Lay Actuary). Imagine you have three archers (red, green and blue arrows) firing arrows at a target. Each archer shoots five times. Finally a fourth archer (black arrows) comes along and shoots an arrow. You have to guess where the centre of his target is. Three examples are shown in Figure 1 below.
In Scenario A it is pretty obvious that the archers are good shots. All their arrows lie close to their individual targets even though you can’t actually see the targets. Although you cannot see the target of the archer firing black arrows, it is pretty clear it must be somewhere close to where the black arrow landed.
In Scenario B all the archers are dreadful shots, your best guess, assuming the targets are somewhere on the post, is to go for the middle of the post.
In Scenario C, the archers are pretty good shots, but it is also clear that all the targets are close to each other. In this case you could form a guess based a compromise - somewhere between the centre of all the shots and where the black arrow fell.
This is the essence of Greatest Accuracy Credibility Theory. We have two pieces of information. The first is the spread of the locations of the targets. We can guess this from the shots that the archers have taken so far. Even if our new archer had not taken any shots at all, we could guess that his target is probably somewhere near where all other targets are.
The second piece of information is how good a shot the archers are – the variability of shots of each individual archer. If the archers are very good shots, we can guess the location of their targets just from their shots.
When the archers are mediocre shots, we should guess somewhere between where the arrow fell and the centre of where the typical targets probably are.
This is the essence of successful fleet rating and is the answer to the question we posed last month. Imagine that each archer represents a fleet and that the height of the arrow up the post represents the amount of claims in any one year. In order to guess the most accurate premium for the “black” fleet, we need to measure the variability of the annual claims within each fleet and also to measure the variability of claims levels between fleets.
Depending on these two pieces of information, the most accurate premium will typically be somewhere between the experience of the fleet and the typical experience of all the fleets. Details of how far in between to go is provided the theory. Poor – and good - claims histories can be due to general volatility in claims experience rather than being signs of inferior or superior risks. The compromise provided by credibility theory creates a smoothing effect and means, that unless it is genuinely appropriate, we will not massively change premiums due to good or bad claims histories.
A while back, this kind of guesswork used to be hard to do. The theory was not well developed and the software was not widely available. Now, the theory is well developed and the software is freely available (R of course – more about that another time). If you are involved in fleet insurance and you don’t do this kind of work – it’s time to start.
I’m looking forward to catching up with you again next month. We’ll move on to farming and the bigger picture. In the meantime if you have any comments, love or hate credibility or simply violently disagree with everything I’ve said – drop me a line at my email address below.
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