Date of this Version
Journal of Optimization Theory and Applications
We consider a class of dynamic advertising problems under uncertainty in the presence of carryover and distributed forgetting effects, generalizing the classical model of Nerlove and Arrow (Economica 29:129–142, 1962). In particular, we allow the dynamics of the product goodwill to depend on its past values, as well as previous advertising levels. Building on previous work (Gozzi and Marinelli in Lect. Notes Pure Appl. Math., vol. 245, pp. 133–148, 2006), the optimal advertising model is formulated as an infinite-dimensional stochastic control problem. We obtain (partial) regularity as well as approximation results for the corresponding value function. Under specific structural assumptions, we study the effects of delays on the value function and optimal strategy. In the absence of carryover effects, since the value function and the optimal advertising policy can be characterized in terms of the solution of the associated HJB equation, we obtain sharper characterizations of the optimal policy.
The final publication is available at Springer via http://dx.doi.org/10.1007/s10957-009-9524-5
stochastic control problems with delay, dynamic programming, infinite-dimensional, bellman equations, optimal advertising
Gozzi, F., Marinelli, C., & Savin, S. (2009). On Controlled Linear Diffusions With Delay in a Model of Optimal Advertising Under Uncertainty With Memory Effects. Journal of Optimization Theory and Applications, 142 (2), 291-321. http://dx.doi.org/10.1007/s10957-009-9524-5
Date Posted: 27 November 2017
This document has been peer reviewed.