Pricing in General Insurance

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Rating Factor Selection and

Generalised Linear Modelling

Plurality is not to be posited without necessity.

—Ockham’s razor

An explanation should be as simple as possible, but not simpler.

—Albert Einstein (abridged)

In situations where a large amount of data is available, such as in personal lines insurance

(and, in some cases, in commercial lines insurance or reinsurance), it is possible to rate

policyholders according to their individual characteristics rather than with a one-size-ts-

all approach.

We are all familiar with this mechanism: the premium that you pay for your car insur-

ance will depend on your age, location, profession and so on. Your household insurance

premium will depend on whether you live along a river or on the top of a hill, and on

whether your roof is made of tiles or of straw; and for commercial insurance, it obviously

makes a difference to your public liability policy if you have an accounting rm or a

nuclear power station.

The characteristics that make a policyholder more or less risky are called ‘risk factors’.

This denition includes everything, whether it is measurable or not. For example, your

riskiness as the owner of a car insurance policy will depend on how aggressive you are

as a driver: however, insurers are unable to measure your aggressiveness. When they give

you a questionnaire, they ask you plenty of questions, but what they would really like

to know is if you are aggressive, reckless, incompetent, and inclined to fall asleep at the

wheel. Because there is no point in asking you those questions, they ask you other, seem-

ingly more innocent questions about other measurable factors that are hopefully a proxy

for your riskiness: age, sex, profession, type of vehicle and the like.

Therefore, you have two types of factors: the factors that really drive the risk (risk fac-

tors) and the factors according to which you are going to be rated (rating factors), as in the

table below.

Risk Factors and Rating Factors

Risk factors Risk factors are the characteristics of the policyholder (individual or company) that make the

policyholder more or less risky, that is, more or less expensive to cover.

Examples: A driver’s recklessness, the position of a house in relation to water hazards

Rating factors Rating factors are the factors that are actually used for pricing a policy, and they are normally

measurable proxies for risk factors (or genuine risk factors when these are measurable).

Examples: A driver’s age, the distance of a house from the river and its altitude