Group for Research in Decision Analysis

G-2017-74

Existence and uniqueness of optimal dynamic pricing and advertising controls without concavity

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We consider a pricing and advertising dynamic-optimization problem where the goodwill dynamics evolve à la Nerlove-Arrow. The firm maximizes its profit over a finite-planning horizon corresponding to the product's lifespan, and it turns out that the Hamilonian is non-concave. We show the existence and uniqueness of an optimal solution under some mild conditions.

, 16 pages