Probabilities of ruin

Abstract

In this article a summing up is made of the author's papers concerning the probability of ruin in a risk business. Results as well as proofs are reviewed. In certain cases not covered in the earlier papers a more systematic treatment is given. Primarily the probability of ruin for a finite time period is dealt with. The corresponding problem for an infinite period is treated as a limit case in a more cursory way. It is throughout assumed that the epochs of claims follow a renewal process, i.e. we adhere to E. Sparre Andersen's model. The case of an ordinary renewal process as well as the case of a stationary such one are treated for both positive and negative capital risks in the spirit of H. Cramer's treatment of the Poisson case. Since the author La. has aimed at facilitating the numerical calculation of ruin probabilities, an essential complement to the article in this respect is the numerical implementation of the author's formulas performed by Nils Wikstad. The reader is, therefore, referred to the latter author's account of numerical methods as well as of numerical results.