The use of discrete moment bounds in probabilistic constrained stochastic programming models

In the past few years, efficient methods have been developed for bounding probabilities and expectations concerning univariate and multivariate random variables based on the knowledge of some of their moments. Closed form as well as algorithmic lower and upper bounds of this type are now available. The lower and upper bounds are frequently close enough even if the number of utilized moments is relatively small. This paper shows how the probability bounds can be incorporated in probabilistic constrained stochastic programming models in order to obtain approximate solutions for them in a relatively simple way.