We consider a dynamic optimization problem where a firm plans their advertising strategy under the uncertainty that their production costs may abruptly increase at any time during the programming interval. We present two approaches that yield a close form solution to this two-stage optimal control problem: a backward approach, where the two periods are solved in reverse order, and a heterogeneous one, where a dedicated version of the maximum principle covers both stages simultaneously. The analytical solution is provided in a simple case, and numerical results are presented for the general case. To evaluate the importance of information about the risk of switching, we compare these results with those of a different scenario, where the planner is unaware of the possible switching time.
(With Alessandra Buratto and Luca Grosset.)