An Axiomatic Foundation for the Theory of Risk Aversion with Applications (working Paper†)

The classic definition of risk aversion, which equates risk aversion with concavity of the utility function, is inherently scale-dependent, in the sense that it is not preserved under monotone (non-linear) transformations of underlying scale, most commonly taken to be money. This limits the notion to monetary, or liquid, goods. We introduce an axiomatic definition of risk aversion, based on the decisions maker’s preference order alone, independent of any numerical scale. We then show that when cast in functional form this axiomatic definition coincides with the classic ArrowPratt definition once the latter is defined with respect to an appropriate “intrinsic” scale (which in general is not money). The applications of the theory are discussed, including, in particular, to disentangling risk aversion from diminishing marginal utility, to multi-dimensional risk aversion, and to the analysis of saving under uncertainty. The entire study is within the expected utility framework.