On convex probabilistic programming with discrete distributions

We consider convex stochastic programming problems with probabilistic const raints involving integer-valued random variables. The concept of a p-effici ent point of a probability distribution is used to derive various equivalen t problem formulations. Next we introduce the concept of r-concave discrete probability distributions and analyse its relevance for problems under con sideration. These notions are used to derive lower and upper bounds for the optimal value of probabilistically constrained convex stochastic programmi ng problems with discrete random variables.