A Multi-Quantile Approach for Open-Loop Stochastic Dynamic Programming Problems*

This paper proposes a multi-quantile approach for solving open-loop continuous-variable discrete-time stochastic dynamic programming problems in systems with non-standard probability distribution functions. Instead of using the expected value of the objective function for building the optimization criterion, the decision maker performs a choice on the decision variables over the objective function value quantiles. The proposed procedure relies on a Monte Carlo simulation of the unknown process input outcomes, associated with an open-loop multiobjective optimization. The optimal control comes from a trade-off analysis that considers, for instance, the risk associated with each policy versus its yield.