Optimal dynamic advertising policies for hereditary processes
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.
integro-differential equations of motion
scientific article; zbMATH DE number 3821431
scientific article