Pricing in General Insurance

157

12

What Is This Thing Called Modelling?

I’m no model lady. A model’s just an imitation of the real thing.

Mae West

Before delving into the details of the pricing process and showing how one can produce a

frequency and severity model of losses, it makes sense to pause and ask ourselves what a

model actually is. In attempting to answer that, it is not easy to go much further, in terms of

philosophical depth, than Mae West: ‘A model’s just an imitation of the real thing’. Others have

viewed models as ‘representations’ (Frigg and Hartmann 2012), citing Bohr’s model of the atom

as one such representation, and yet others have referred to them as ‘metaphors’ (Derman 2010).

More precise mathematical denitions of ‘model’ are also available: for example, a statistical

model can be dened as a mathematical description of the relationship between random vari-

ables or more formally as a collection of probability distributions (see Wikipedia, ‘Statistical

model’, http://en.wikipedia.org/wiki/Statistical_model).

My favourite denition of model, however, is this:

A model is a simplied description of reality.

This denition captures the ‘imitation’ concept and the nature of the relationship

between model and reality but also reminds us that models are approximations and as

such, we should always be aware of their limitations: something which is not obvious from

the more formal denitions of models.

In this chapter, we look at these ideas in more depth, and we will explain what the mod-

elling approach entails in practice and why we need to use modelling at all. We will also

provide a quick foray into how the problem of selecting a good model, mostly extracted

from Parodi (2011).

At the end of this very brief chapter, we will have hopefully planted the seeds of some

healthy distrust for the predictive power of complex, clever models and will have clearer

ideas on what modelling is actually about. These ‘seeds of distrust’ will then be developed

in following chapters on frequency (Chapter 14) and severity models (Chapter 17) and on

measuring uncertainty (Chapter 18).

12.1 Why Do We Need Modelling at All?

We have explained above what a model is, but we have yet to mention why modelling is

needed at all. We will try to explain that with a simple example in Section 12.1.1, and in

Section 12.1.2 we will mention other uses of models.