Optimal dynamic advertising policies for hereditary processes
type: Item
instance of: scholarly article
title: Optimal dynamic advertising policies for hereditary processes
zbMATH Open document ID: 0518.90040
DOI: 10.1007/BF00934746
author: Richard F. Hartl
published in: Journal of Optimization Theory and Applications
publication date: 1984-01-01T00:00:00Z
review text: In this paper, the Nerlove-Arrow model of optimal dynamic advertising policies is generalized by assuming a general probability distribution of the ``forgetting time'', rather than the exponential one. A control problem with integro-differential equations of motion is defined for which the transitory and steady-state properties of the optimal advertising policy are examined. The effects of assumptions like IHR distributions DHR distributions, the existence of an upper bound for the forgetting time, etc, are explained. It is shown that there are two (in the case of an exponential distribution even three) different current-value adjoint functions associated with the problem and relations between the two (three) are established. Also provided is a sensitivity analysis.
Mathematics Subject Classification ID: 90B60
Mathematics Subject Classification ID: 91B62
Mathematics Subject Classification ID: 49K21
zbMATH DE Number: 3821431
zbMATH Keywords: hereditary processes
zbMATH Keywords: marketing
zbMATH Keywords: Nerlove-Arrow model
zbMATH Keywords: optimal dynamic advertising
zbMATH Keywords: forgetting time
zbMATH Keywords: integro-differential equations of motion
zbMATH Keywords: transitory and steady-state properties
zbMATH Keywords: existence of upper bound
zbMATH Keywords: sensitivity analysis
zbMATH Keywords: time lags
zbMATH Keywords: optimal control
Wikidata QID: Q59389981
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3821431