Pricing in General Insurance

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18

Identifying, Measuring and

Communicating Uncertainty

In the previous chapters, we learned how to produce a stochastic model for our aggregate

losses, which encapsulates our prediction for the losses in the next policy period. On the

basis of this model, underwriters and clients may (if they trust us) take decisions on how

much premium to charge (underwriters), whether to buy a policy and how much risk to

retain (clients) and so on.

It is only fair to communicate how accurate our predictions are. A statement such as, ‘the

expected losses to this policy for the year 2012 are £1.62M’ is neither right nor wrong if you

are not also able, to some extent, to assess the error on your estimate: because saying that the

expected losses are £1.62 ± £0.01M is very different from saying that they are £1.62 ± £1M!

Things get more confusing because we are not speaking of deterministic quantities such

as your weight, but of the mean of a stochastic variable that uctuates widely, so it may

take several years to realise that an estimate may be materially wrong.

We have several types of uncertainty that we need to address in actuarial practice:

• Process uncertainty

• Parameter uncertainty

• Model uncertainty

• Assumption/data uncertainty

• Approximation errors in calculations

We are now going to look at each type of uncertainty in turn. After a few words of

explanation, we will explain how to calculate the effect of that type of uncertainty on pric-

ing and we will briey comment on how that type of uncertainty can be communicated

to a non-technical audience: a section on communicating uncertainty has been included

because it is one of the things that the actuary is explicitly required to do in formal reports

and because it is also something that is quite challenging.

In dening the various types of uncertainty, it is useful to keep the following simple

examples in mind:

Example 1: Consider the yearly number of claims related to a risk. Assume that the

number of claims follows a Poisson distribution and that the Poisson rate is esti-

mated based on the number of claims observed over a past period.

Example 2: Consider the distribution of loss severities for a given risk. Assume that

the loss amounts follow a lognormal distribution and that the parameters of the

lognormal distribution are calculated based on a number of claims observed over

a past period. Also, consider that the nal loss amount of some of the claims is not

known yet – only a reserve estimate is available.