Pricing in General Insurance

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Pricing Process: A Gentle Start

Pricing is a complex endeavour, which is best conceptualised as a process or even as a

project: that is to say, an undertaking with a beginning and an end and a number of dif-

ferent tasks to be executed in a certain order. To get a fair idea of what the pricing process

entails without getting bogged down into the details that inevitably need to be considered

in any realistic example, we will start looking at a very simple example of pricing, car-

ried out in a rather traditional, non-actuarial way. Despite its simplicity, this example will

contain all the main ingredients of the pricing process that we will expand on in the rest

of the book.

1.1 An Elementary Pricing Example

Suppose you are an underwriter working for a commercial insurer and you are asked to

insure a company for employer’s liability. Also assume that you have agreed to insure only

95% of each loss, so that the insured has an active interest in keeping the number of claims

low.* We also assume that only up to £10M for each loss and in aggregate is awarded (after

taking the 95% cut).

The prospective insured has given you the following table (Figure 1.1), which gives you

the total losses incurred by year, from the ground up, before taking insurance into consid-

eration. (Although this sounds reasonable, it is actually quite unusual for an insured to be

able to give you a well-structured data set with their losses. More likely, insurance com-

panies or claims management companies will have collected them and will have shared

them with the insured.)

What price do you think the insured should pay for cover in 2015 (assume that the policy

will incept on 1 January 2015 and will last one year)? It is not possible to answer this ques-

tion directly at this stage. For one thing, the price is a commercial decision, which depends

on many factors, the main one being: how much money do I want to make (on average) by

selling this insurance?

So let us rephrase the question: assuming that my expenses (such as the expenses of

dealing with policies and claims) are roughly 15% of the premium, and that I want 10%

prot, how much should I charge for this policy?

A naïve method that comes to mind to reply to the question above is simply to average

the total losses over the period 2005 to 2014. This yields the numbers in Figure 1.2:

*

This is not a common insurance structure for employer’s liability insurance in the United Kingdom and is not

legal unless the amount retained is retained by the client through a direct-writing captive domiciled in the

European Union (employers’ liability policies have to be sold from the ground up and 100% of each loss has

to be insured, up to a certain limit). However, the reason for using this structure here is that it allows us to

explain the stages of the rating process with an uncomplicated example.