The portfolio selection problem is traditionally modelled by two different approaches. The first one is based on an axiomatic model of risk-averse preferences, where decision makers are assumed to possess an expected utility function. The second approach, first proposed by Markowitz (1952), reduces the portfolio choice to a set of two criteria, reward and risk. Usually the reward-risk model is not consistent with the first approach, even when the decision is independent from the specific form of the risk-averse expected utility function. In this paper we generalize the reward-risk model for portfolio selection. We define reward measures and risk measures by giving a set of properties these measures should satisfy. One of these properties will be the consistency with second order stochastic dominance, to obtain a link with the expected utility portfolio selection. We characterize reward and risk measures and we discuss the implication for portfolio selection.