The axiomatic basis of risk–value models

Due to their simplicity and intuitive plausibility, risk–value models have often been employed to represent individual choice behavior under risk in finance and management science. Nevertheless, an axiomatic foundation of risk–value models is still missing in the literature and the present paper tries to provide a first step in order to fill this gap. Therefore, an axiomatization of one specific class of risk–value models is derived. This special class is characterized by risk measures which satisfy the following convexity property; if two lotteries have identical risk then every probability mixture of these lotteries must also have the same risk. Among others, value-at-risk, first partial moments, and safety-first risk measures satisfy this convexity property while the variance does not. It will be shown that a weakened variant of the Independence axion allows to characterize the considered class of risk–value models which implies that they should be integrated in the literature on non-expected utility theory.