Abstract When uncertainty is associated with some intrinsically relevant states of nature, there is no reason for an agent to base his or her preferences only on probability distribution of claims. We propose a new concept of risk for state-contingent claims that, unlike the standard concept of Rothschild–Stiglitz, does not identify state-contingent claims with their probability distribution. This concept is called mean-independent risk, and we provide a simple characterization in terms of marginal utilities of (non-expected) utility functions that exhibit aversion to mean-independent risk. We study implications of aversion to mean-independent risk on agents’ choices under uncertainty. Content Type Journal Article Category Research Article DOI 10.1007/s00199-008-0388-y Authors Jan Werner, University of Minnesota Department of Economics Minneapolis MN 55455 USA Journal Economic Theory Online ISSN 1432-0479 Print ISSN 0938-2259 ...