Traditional models in multistage stochastic programming are directed to minimizing the expected value of random optimal costs arising in a multistage, non-anticipative decision process under uncertainty. Motivated by risk aversion, we consider minimization of the probability that the random optimal costs exceed some preselected threshold value. For the two-stage case, we analyse structural properties and propose algorithms both for models with integer decisions and for those without. Extension of the modeling to the multistage situation concludes the paper.