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The problems of linear stochastic model optimization are considered using quantile and probability criterions. The a priori information about the distribution law of the model random coefficients is defined by certain constraints on the first- and second-order moments. The concept of the minimax strategy is formulated and the last one is constructed using the convex programming duality theory. The analytic dependence of the minimax strategy on the solution of the dual problem is derived. A computational procedure for solving the dual problem is examined. The results of computer modeling are presented.