The stochastic goodwill problem

Stochastic control problems related to optimal advertising under uncertainty are considered. In particular, we determine the optimal strategies for the problem of maximizing the utility of goodwill at launch time and minimizing the disutility of a stream of advertising costs that extends until the launch time for some classes of stochastic perturbations of the classical Nerlove–Arrow dynamics. We also consider some generalizations such as problems with constrained budget and with discretionary launching.