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Optimal advertising in exponentially decaying markets. (English) Zbl 0797.90055

Summary: An optimal advertising singular control problem with unbounded control is formulated in a generalized fashion by introducing a reparametrization of time. This reparametrization is a new control. The method of dynamic programming is then used to determine the optimal synthesis. Afterward, it is easy to drop the reparametrization of time. In this interpretation, the synthesis shows an impulsive control at the initial time.

MSC:

90B60 Marketing, advertising
49L20 Dynamic programming in optimal control and differential games
49N25 Impulsive optimal control problems
93C95 Application models in control theory
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References:

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