Some problems in the collective theory of risk

In most works treating the ruin problem of an insurance company, the probability of ruin some time in the future is chiefly considered. The time variable is thus eliminated, which in most respects simplifies the problem theoretically. But as well from theoretical as from practical points of view it is also of interest to know the probability of ruin before a certain point of time. This subject has been more closely dealt with by Tryggwe Saxén [1]Footnote 1 for insurance with only negative sums at risk. In this paper we shall treat the same problem for positive risk sums, especially when the risk sum distribution can be represented by an exponential function.