Abstract. The problems of finding the optimal portfolio decisions on the reward–risk ratio under conditions of risk and partial uncertainty are analyzed. It is shown how such problems can be reduced to linear programming problems, both in the case of known distributions of random variables and in the case of imprecise probabilities of scenarios. A set of application examples is considered. Refs: 31 titles.

Keywords: polyhedral coherent risk measure, conditional VaR, spectral risk measure, portfolio optimization, reward–risk ratio, efficiency measure.