The Stochastic Goodwill Problem

Abstract

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. We also consider some generalizations, such as problems with constrained budget, optimization under partial information, and discretionary launching.

Keywords: optimal advertising, new product introduction, linear quadratic regulator, stochastic control, discretionary stopping