Pricing in General Insurance

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3

The Policy Structure

The ideal insurance product, from a consumer’s point of view, would be a contract that

went something like this: ‘We agree to insure your car (or your house, or your pet, or your

company) and compensate you for whatever happens to the car and whatever damage or

injury you cause with it to a third party. We will pay the full amount whether it is 20p or

£200M (the sky’s the limit, really) under all circumstances, no questions asked’.

If you have ever gone through a policy contract, you will have noticed that it does not

quite read like that. The most notable feature of an insurance policy is perhaps that it has

many exclusions: for example, cover may be limited or even withdrawn if you drink and

drive, or if you deliberately jump off a bridge, or if you drive whilst a civil war is raging, or

even if you do nothing more reckless than going abroad.

It is not always easy to assess the effect of exclusions in a quantitative way, and very

often actuaries nd themselves in the position of having to assume that the policies they

are pricing have a standard wording and that the wording does not change over the years.

However, changes in wording do have an effect and wherever possible they have to be

borne in mind by the discerning actuary.

This chapter is concerned with one specic type of exclusion that has paramount impor-

tance for pricing actuaries and whose effect can be assessed with actuarial techniques:

these are the coverage modiers, such as excesses and limits. For example, your car policy

might require that you bear the cost of the rst £250 of each claim and those exceeding

£800 for your car radio. All these coverage modiers have been collated here under the

heading of ‘policy structure’.

Understanding policy structure is essential for pricing because in almost all cases the

cost of risk, which is the most relevant, is almost never the gross amount of a loss but the

amount that is paid by an insurer.

Policy structures tend to be quite different depending on who the policyholder is: we

have therefore subdivided the treatment of this into three headings: personal lines (in

which the policyholders are individuals), commercial lines (in which the policyholders

are corporate entities, ranging from multinationals such as Coca-Cola to small companies,

charities and sole traders) and reinsurance (in which the policyholders are insurers or

evenreinsurers).

Let us start with the simplest case – that in which the policyholders are individuals.

3.1 Personal Lines

For personal lines, the most common coverage modications are rather simple: normally,

there is a deductible (excess) and a policy limit. If there is any complication is because there