The aim of this study is to find suitable methods for utilizing available statistical information on the risk development of terminated insurances. This information may comprise not only data respecting sex, age, insurance tariff, etc., but also the points of time when certain events—disability, injuries or damages—have occurred as well as their durability and cause. The method study here presented is based on statistical material gathered from long-term disability insurances which have ceased to be valid, either in consequence of the expiration of the term of insurance, or the insured's death. We endeavour to study the point of time when the first event (disability) occurred and the relation between subsequent events, searching suitable methods for assessing risks after the occurrence of the primary event.

The influence of passed events upon the future risk process may be explained by either a direct dependence between actual events—actual damage or disability may have an impairment for the future of the risk—or by heterogeneity a priori. In the former case, we may speak of a contagious process (Polya-Eggenberger), and, in the latter case, the occurrence or non-occurrence of an event may, according to Lexis and Newbold, act as a risk differentiating factor providing a theoretical basis for a technique of experience rating.

It is difficult to decide whether the relationship noted in respect of a risk process is of the direct or the indirect kind. A direct dependence between one event and the following ones has no relevance to a study of the incidence of the first event and the time of its occurrence. We avoid in such a study the obstacles created by formal rules and regulations with regard to the problem of whether two or more disability periods occurring at short intervals should be considered as a single disability period or not. In order to measure the frequency of the first event we have—as in the case of measuring mortality—to limit the period exposed to risk until the occurrence of the first event.