Optimal distributed dynamic advertising

Details Optimal distributed dynamic advertising Optimal distributed dynamic advertising

2004-06-22

arxiv.org/abs/math/0406435v2

Mathematics

Optimization and Control

21 pages, no figures

Scientific paper

We propose a novel approach to modeling advertising dynamics for a firm operating over distributed market domain based on controlled partial differential equations of 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 general characterization of the optimal solutions. Sharper, feedback-form, characterizations of the optimal solutions are obtained for two variants of the general problem.

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