Abstract. The author considers the use of risk measures that allows combining stochastic programming and robust optimization problems within the overall approach. Constructions for the class of polyhedral coherent risk measures are described. It is shown how the use of such measures can reduce problems of linear optimization under uncertainty to deterministic linear programming problems.

Keywords: stochastic programming, robust optimization, polyhedral coherent risk measure, conditional value-at-risk, spectral coherent risk measure, imprecise probabilities, linear programming.