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Application of Reliability Theory to Insurance

Published online by Cambridge University Press:  29 August 2014

E. Straub*
Affiliation:
Swiss Reinsurance Company, Zurich
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1. There is a general rule applicable to all insurance and reinsurance fields according to which the level of the so-called technical minimum premium should be fixed such that a certain stability criterion is satisfied for the portfolio under consideration. The two bestknown such criteria are

(i) the probability that there is a technical loss in any of the future years should be less than a given percentage

(ii) the probability that the company gets “ruined” i.e. initial reserves plus accumulated premiums minus accumulated claims becomes negative at any time of a given period in the future should be less than a tolerated percentage.

Confining ourselves to criterion (i) in the present paper we may then say that the problem of calculating technical minimum premiums is broadly spoken equivalent with the problem of estimating loss probabilities. Since an 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 paper without having had the opportunity of numerous discussions with the Reliability experts R. Barlow and F. Proschan while I was at Stanford University. In particular I was told the elegant proof of theorem 3 given below by R. Barlow recently.

Type
Research Article
Copyright
Copyright © International Actuarial Association 1971

References

[1]Barlow, R, Proschan, F and Hunter, L, Mathematical Theory of Relıabılıty Theory, John Wıley and SonsGoogle Scholar
[2]Barlow, R and Zwet, W van, Asymptotıc propertıes of ısotonıc estı-mators for the generalızed faılure rate, Part I, Berkeley 1969Google Scholar
[3]van Zwet, W, Convex transformatıons of random varıables, Mathe-matıcal Centre, Amsterdam 1964Google Scholar
[4]Morey, R, Some stochastıc propertıes of a compourd renewal damage model, Operatıons Research 1967(?)Google Scholar