Risk and Uncertainty Aversion on Certainty Equivalent Functions

Abstract

The notion of risk aversion was originally developed with reference to the Expected Utility model. de Finetti (1952), Pratt (1964) and Arrow (1965) associated the concavity of the von Neumann-Morgenstern utility function with some relevant aspects of the decision-maker’s preferences. In particular, risk aversion can be defined in terms of risk premium (i.e., the difference between the expected value and the certainty equivalent of a lottery). With reference to the EU model the risk premium is nonnegative for all lotteries if and only if the von Neumann-Morgenstern utility function is concave. However, with reference to the EU model, other relevant aspects of the preferences also depend on the concavity of the utility function: for instance, if we compare two lotteries of which one has been obtained from the other through mean preserving spreads, the less risky lottery is (weakly) preferred for all pairs of lotteries of this kind if and only if the von Neumann-Morgenstern utility function is concave. Moreover, the EU model does not imply that a randomization of lotteries matters (for instance, according to the EU model, a lottery whose consequences are a randomization of the outcomes of two equally preferred lotteries is indifferent to them), while the possibility that a decision-maker prefers not to be involved in an additional lottery could be considered as a kind of risk aversion. Taking into consideration more general models than the EU model, it is no longer true that risk aversion only consists of positive risk premia and of aversion to riskier (in the sense of mean preserving spreads) lotteries and that these two risk aversions depend on the same characteristic of decision-maker’s preferences.