We consider stochastic programming problems with probabilistic constraints
involving integer-valued random variables. The concept of a p-efficient poi
nt of a probability distribution is used to derive various equivalent probl
em formulations. Next we introduce the concept of r-concave discrete probab
ility distributions and analyse its relevance for problems under considerat
ion. These notions are used to derive lower and upper bounds for the optima
l Value of probabilistically constrained stochastic programming problems wi
th discrete random variables. The results are illustrated with numerical ex
amples.