Premium principles and translation invariance
type: Item
instance of: scholarly article
title: Premium principles and translation invariance
zbMATH Open document ID: 0557.62085
DOI: 10.1016/0167-6687(84)90019-2
author: Axel Reich
published in: Insurance Mathematics \& Economics
publication date: 1984-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 62P05
Mathematics Subject Classification ID: 91B16
zbMATH DE Number: 3888765
zbMATH Keywords: translation invariance
zbMATH Keywords: premium principles
zbMATH Keywords: risk aversion
zbMATH Keywords: utility functions
MaRDI profile type: Publication
full work available at URL: 0167-6687(84)90019-2
OpenAlex ID: W2033319326
cites work: Q5612652
cites work: Q3868650
cites work: Q3853027
cites work: Q3314810
cites work: A new premium calculation principle based on Orlicz norms
cites work: Q3252995
cites work: Q5525025
description: scientific article; zbMATH DE number 3888765