Risk theory is usually developed within probability theory. The aim of this paper is to propose ail approach of the risk aversion by possibility theory, initiated by Zadeh in 1978. The main notion studied in this paper is the possibilistic risk premium associated with a fuzzy number A and a utility function it. Under the hypothesis that the utility function it verifies certain hypotheses, one proves a formula to evaluate the possibilistic risk premium in terms of it and of some possibilistic indicators, (C) 2008 Elsevier B.V. All rights reserved.