We propose a stochastic optimization model for the Multiperiod Multiproduct Advertising Budgeting problem, so that the expected profit of the advertising investment is maximized. The model is a convex optimization problem that can readily be solved by plain use of standard optimization software. It has been tested for planning a realistic advertising campaign. In our case study, the expected profit of the stochastic approach has been favorably compared with the expected profit of the deterministic approach. This provides a quantitative argument in favor of the stochastic approach for managerial decision making in a data-driven framework.