Premium principles and translation invariance
Classical premium principles are investigated with respect to the property of translation invariance, i.e. (1) \(\Pi (X+c)=\Pi (X)+c\). As one can expect, most premium principles involving risk aversion (in a utility-theoretical sense, i.e. the mean value, Swiss and Orlicz principles) are not translation-invariant, unless the underlying utility functions are trivial (linear) or very simple (exponential). Furthermore, it is shown that the above mentioned principles are highly translation - not invariant, in the sense that as soon as (1) holds for one or two particular values of c, then the utilities are linear or exponential. The author does not comment his mathematical results; the main concluding remark probably should be that, as far as utility theory is to be considered, translation invariance is a rather undesirable property.
scientific article; zbMATH DE number 3888765