Economic and financial activities are often influenced simultaneously by a decision and random factors. Since the decision parameter must be constructed mostly without knowledge of a random element realization, an optimization problem depending on a probability measure corresponds to this situation. Usually in applications this measure must be replaced by an empirical one. The aim of the proposed grant project is to continue and extend stochastic optimization models. To this end we employ results from the stochastic programming (one-stage and multistage, one objective and multiobjective), Markov decision processes and empirical processes. The risk measures and stochastic dominance appear in the proposed project not only in the objective functions but also in the constraints conditions.