Risk and risk aversion when states of nature matter

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.