An insurer is in business to provide insurance cover against specified risks. The insurer offers to provide a policy with certain benefits under particular conditions, and contracts to do this at a stated price, the premium. The customer may or may not accept the offer – if the contract is accepted and the premium is paid, the customer becomes the policyholder.

In this chapter we consider various pricing principles on which a general (non-life) insurer may base the premiums to be charged. We consider the premium based on the profile of the risks involved alone, not inflated or otherwise adjusted for the insurer's running costs or profit margins or other external considerations (such as competition in the marketplace).

In §4.1 we consider six principles based on the summary properties of the distribution of the random variable representing the risk. Two of these cases involve the insurer's view of the utility of the risk – an introduction to utility theory is given in Appendix A.

In §4.2 we consider the maximum and minimum premiums which are consistent with utility principles.

In §4.3 to §4.7 we consider an important branch of actuarial science called credibility theory, which consists of applications of Bayesian statistics in a general insurance context. The methods are concerned with setting a premium for a risk, taking into account the recent claims experience of the risk (and usually that of other comparable risks) – this methodology provides a major illustration of experience rating.