Contributions to the theory of stochastic programming

Two s t o c hastic programming decision models are presented. In the rst one, we use probabilistic constraints, and constraints involving conditional expectations further incorporate penalties into the objective. The probabilistic constraint prescribes a lower bound for the probability of simultaneous occurrence of events, the number of which can be innnite in which c a s e s t o c hastic processes are involved. The second one is a variant of the model: two-stage programming under uncertainty, where we require the solvability of the second stage problem only with a prescribed (high) probability. The theory presented in this paper is based to a large extent on recent results of the author concerning logarithmic concave measures.