The insurer's ruin

This paper was written in connection with the preparation of Marché Commun regulations in the insurance sector and has been submitted to the Commission Technique pour l'étude d'un indice de solvabilité relatif aux entreprises d'assurances contre les dommages. It aims at explaining the scope of the problem to non-mathematicians and for that reason emphasizes its logical in contradistinction to its computational aspects.The probability of the insurer's ruin has two aspects. The occurrence of the event ruin may be considered with respect to a fixed period but also with respect to a period of undetermined length. In both cases the period starts at a moment at which the insurer's capital (patrimoine) is known and it is intuitively clear that in both cases the probability of ruin will be the higher as the insurer's capital is smaller and the risk to which he is exposed heavier.For some purposes more precise conclusions are required. This requirement gives rise to problems which will be considered here with respect to the probability of the occurrence of ruin in a period of undetermined length. It will be taken for granted that besides the artificial events occurring in games of chance there are other classes of uncertain events to which numerical probabilities can be assigned and that, as far as claims are concerned, the insurer's losses belong to one of the said classes. On this understanding it makes sense to consider a numerical probability of ruin depending on a fixed initial capital, random losses to which numerical probabilities are assigned, and other profits and losses.