Risk premiums and benefit measures for generalized-expected-utility theories

Standard tools for the analysis of economic problems involving uncertainty, including risk premiums, certainty equivalents and the notions of absolute and relative risk aversion, are developed without making specific assumpti ons on functional form beyond the basic requirements of monotonicity, trans itivity, continuity, and the presumption that individuals prefer certainty to risk. Individuals are not required to display probabilistic sophisticati on. The approach relies on the distance and benefit functions to characteri ze preferences relative to a given state-contingent vector of outcomes. The distance and benefit functions are used to derive absolute and relative ri sk premiums and to characterize preferences exhibiting constant absolute ri sk aversion (CARA) and constant relative risk aversion (CRRA). A generaliza tion of the notion of Schur-concavity is presented. If preferences are gene ralized Schur concave, the absolute and relative risk premiums are generali zed Schur convex, and the certainty equivalents are generalized Schur conca ve.