Optimal Distributed Dynamic Advertising
University of Bonn - Institut fuer Angewandte Mathematik
Columbia University - Columbia Business School; University of Pennsylvania - Operations & Information Management Department
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.
Number of Pages in PDF File: 23
Keywords: optimal advertising, new product introduction, distributed control, infinite-dimensional analysis, linear-quadratic control, partial differential equationsworking papers series
Date posted: October 7, 2004
© 2013 Social Science Electronic Publishing, Inc. All Rights Reserved.
This page was processed by apollo4 in 0.422 seconds