Decision under risk and certainty effect: A general axiomatic model

Due to the inability of the classical model of von Neumann and Morgenstern to take into account the certainty effect, Jaffray has developed a model of rational behavior under objectively probabilized uncertainty. However, the latter model only covers the case of lotteries (probability distributions of finite support). In this paper, we propose a generalisation of this model to the case of arbitrary probability distributions, based on four axioms having a precise mathematical content and interpretation. We show that choices are partially determined by an arbitration between the level of security and the expected utility.