When the word statistics is used in connexion with non-life insurance the first reaction of most of those concerned with the day-today requirements of the business is to think in terms of the relationship between premiums and claims. In my talk tonight I shall not be concerned with this aspect but will be concerned with the structure of the risk processes underlying the business. In order to try to bring out some of the essential characteristics I have used the minimum of mathematics, using numerical examples to illustrate the points. Furthermore, in order to limit my talk to a reasonable time and to make it ‘live’ I have deliberately omitted many of the finer points which arise in practice to which regard must be had in using mathematical or statistical models to describe the actual situation.

At rock bottom the insurance industry rests on the operation of laws of chance. A hazard is recognized as being liable to give rise to a potential pecuniary liability, and in no time at all someone is prepared to provide a policy against such liability. In devising the policy, and in assessing the rate of premium to be charged, it is necessary to define the event which must happen before a claim can be admitted under the policy and to be satisfied that the happening of the event is fortuitous as far as the proposer is concerned. In life insurance difficulty seldom arises under either count but in non-life insurance the position is frequently very troublesome.