The Utility Concept Applied to the Theory of Insurance

Abstract

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.