, Volume 29, Issue 4, pp 615-627

Optimal advertising policy with the contagion model

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Abstract

This paper considers an optimal control problem for the dynamics of a contagion model, the optimal control being the rate of advertising expenditure that maximizes the present value of net profit streams over an infinite horizon. By using a Green's theorem approach, it is shown that there are multiple optimal stationary equilibria and that the optimal path from any given initial condition is a nearest feasible path to one of these equilibria.

Communicated by J. V. Breakwell
This work was partially supported by the National Research Council of Canada, Grant No. A4619.