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.