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The Utility Concept Applied to the Theory of Insurance

Published online by Cambridge University Press:  29 August 2014

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In some recent papers ((1), (2) and (3)) about reinsurance problems I have made extensive use of utility concepts. It has been shown that if a company follows well defined objectives in its reinsurance policy, these objectives can be represented by a utility function which the company seeks to maximise. This formulation of the problem will in general make it possible to determine a unique reinsurance arrangement which is optimal when the company's objectives and external situation are given.

More than 50 years ago Guldberg (4) wrote (about the probability of ruin): “Wie hoch diese Wahrscheinlichkeit gegriffen werden soil, muss dent subjektiven Ermessen oder von Aussen kommenden Bedingungen überlassen bleiben”. This is the traditional approach to reinsurance problems. It does obviously not lead to a determinate solution. Most authors taking this approach conclude their studies by giving a mathematical relation between some measure of “stability”, such as the probability of ruin, and some parameter, for instance maximum retention, to which the company can give any value within a certain range. Such studies do usually not state which particular value the company should select for this parameter, i.e. what degree of stability it should settle for. This question is apparently considered as being outside the field of actuarial mathematics.

Type
Research Article
Copyright
Copyright © International Actuarial Association 1961

References

REFERENCES

(1)Borch, Karl: “An Attempt to Determine the Optimum Amount of Stop Loss Reinsurance”, Transactions of the XVIth International Congress of Actuaries, Vol. 2, pp. 597610.Google Scholar
(2)Borch, Karl: “Reciprocal Reinsurance Treaties”, The Astin Bulletin, Vol. I, pp. 170191.Google Scholar
(3)Borch, Karl: “Reciprocal Reinsurance Treaties seen as a Two-person Co-operative Game”, Skandinavisk Aktuarietidskrift, 1960, pp. 2958.Google Scholar
(4)Guldberg, Alf: “Zur Theorie des Risikos”, Reports of the Sixth International Congress of Actuaries, Vol. I, pp. 753764.Google Scholar
(5)Markowitz, Harry: Portfolio Selection, John Wiley & Sons, 1959.Google Scholar
(6)Neumann, J. von and Morgenstern, O.: Theory of Games and Economic Behavior, Princeton 1944.Google Scholar
(7)Shackle, G. L. S.: Expectation in Economics, Cambridge 1949.Google Scholar