Optimal distributed dynamic advertising. (English) Zbl 1279.90085
Summary: We propose a novel approach to modeling advertising dynamics for a firm operating over a distributed market domain based on controlled partial differential equations of the diffusion type. Using our model, we consider a general type of finite-horizon profit maximization problem in a monopoly setting. By reformulating this profit maximization problem as an optimal control problem in infinite dimensions, we derive sufficient conditions for the existence of its optimal solutions under general profit functions, as well as state and control constraints, and provide a general characterization of the optimal solutions. Sharper, feedback-form characterizations of the optimal solutions are obtained for two variants of the general problem.
MSC:
| 90B60 | Marketing, advertising |
| 49K20 | Optimality conditions for problems involving partial differential equations |
| 49N10 | Linear-quadratic optimal control problems |
| 91B62 | Economic growth models |
Keywords:
Optimal advertising; New product introduction; Distributed control; Infinite-dimensional analysis; Linear-quadratic controlReferences:
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