Optimization of a single-step investment strategy by a quantile criterion is studied. The a priori information on the distribution law for the vector of effective financial instruments is defined by certain constraints on the first- and second-order moments. The concept of a minimax investment strategy is formulated, and the strategy is constructed using the convex programming duality theory. For a set of admissible strategies defined by constraints in the form of linear equalities and inequalities, the minimax strategy is constructed with the help of an analytical dependence on the solution of the dual problem. The existence and uniqueness of the minimax quantile strategy are studied. A computation procedure for solving the dual problem is described. Results of a numerical modeling experiment are given.
