On stochastic linear programming problems with the quantile criterion

We study qualitative properties of a stochastic linear programming problem with quantile criterion for a wide class of distributions. We show convexity conditions for the criterion function with respect to the strategy, and continuity conditions with respect to the strategy and reliability level. We give sufficient conditions for the existence of a solution. We present a new algorithm for finding a guaranteeing solution of the problem, i.e., an admissible solution for which the quantile criterion function's value turns out to be close to optimal.