The hardest part of modelling decision-making problems in the real world, is the uncertainty associated to realizations of futures events. The stochastic programming is responsible about this subject; the target is finding solutions that are feasible for all possible realizations of the unknown data, optimizing the expected value of some functions of decision variables and random variables. The approach most studied is based on Monte Carlo simulation and the Sample Average Approximation (SAA) method which is a kind of discretization of expected value, considering a finite set of realizations or scenarios uniformly distributed. It is possible to prove that the optimal value and the optimal solution of the SAA problem converge to their counterparts of the true problem when the number of scenarios is sufficiently big. Although that approach is useful, there exist limiting factors about the computational cost to increase the scenarios number to obtain a better solution; but the most important fact is that SAA problem is function of each sample generated, and for that reason is random, which means that the solution is also uncertain, and to measure its uncertainty it is necessary consider the replications of SAA problem to estimate the dispersion of the estimated solution, increasing even more the computational cost. The purpose of this work is presenting an alternative approach based on robust optimization techniques and applications of Jensen s inequality, to obtain bounds for the optimal solution, partitioning the support of distribution (without scenarios creation) of unknown data, and taking advantage of the convexity. At the end of this work the convergence of the bounding problem and the proposed solution algorithms are analyzed.