Dual Moments and Risk Attitudes

Abstract

The well-known Pratt–Arrow approximation, developed independently by John W. Pratt and Kenneth Arrow, provides an insightful dissection of the risk premium under the expected utility (EU) model. It is given by one-half the product of the variance of the risk and the local index of absolute risk aversion of the decision maker. Quite surprisingly, despite many important developments on “global” risk aversion in non-EU models, the “local” approach to risk aversion has received little attention outside EU. By considering the first two dual moments, mean and maxiance, on equal footing with the first two primal moments, mean and variance, the authors develop a dissection of the risk premium under the popular rank-dependent utility (RDU) model. This yields a simple approximation to the risk premium and a local index of absolute risk aversion under the RDU model.

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