Existence and uniqueness of optimal dynamic pricing and advertising controls without concavity |
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Authors: | Bertrand Crettez Naila Hayek Georges Zaccour |
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Institution: | 1. Université Panthéon-Assas, Paris II, CRED, France;2. GERAD, HEC Montréal, Canada |
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Abstract: | 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 Hamiltonian is non-concave. We show the existence and uniqueness of an optimal solution under some mild conditions. |
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Keywords: | Advertising Pricing Goodwill stock Nerlove–Arrow dynamics |
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