ISSN:
1573-2878
Keywords:
Advertising
;
time lags
;
integrodifferential equations
;
hereditary processes
;
optimal control
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract 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 integrodifferential 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 and 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00934746
