A Conceptual Foundation for the Theory of Risk Aversion

Classically, risk aversion is equated with concavity of the utility function. In this paper we explore the conceptual foundations of this definition. In accordance with neo-classical economics, we seek a scale-free definition of risk aversion, based on the decisions maker’s preference order alone, independent of numerical values. We explore two such definitions. We then show that when cast in quantitative form these ordinal definitions coincide with the classical Arrow-Pratt definition once the latter is defined with respect to the appropriate scale (which, in general is not money), thus providing a conceptual foundation for the classical definition. The implications of the theory are discussed, including, in particular, to defining risk aversion for non-monetary goods, to disentangling risk aversion from diminishing marginal utility, to multi-commodity/multi-period risk aversion, and to inter-temporal discounting. The entire study is within the expected utility framework.