Appl[cation of Re1aabil[ty Theory to Insurance

Confining ourselves to criterion (i) in the present paper we may then say that tile problem of calculating technical minimuna premiums is broadly spoken equivalent with the problem of estimating loss probabilities. Since art exact calculation of such probabilities is only possible for a few very simple and therefore mostly unrealistic risk models and since e.g Esscher's method is not always very easy to apply in practice it might be worthwhile to describe in the following an alternative approach using results and techniques from Reliability Theory in order to establish bounds for unknown loss probabilities. It would have been impossible for me to write this 1)aper without having had the opl)ortunity of numerous discussions with the Reliahility experts R. Barlow and F. Proschan while I was at Stanford University. In particular I was told tile elegant proof of theorem 3 given below by R. Barlow recently.