Operations, Information and Decisions Papers

Document Type

Journal Article

Date of this Version

8-2009

Publication Source

Journal of Optimization Theory and Applications

Volume

142

Issue

2

Start Page

291

Last Page

321

DOI

10.1007/s10957-009-9524-5

Abstract

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.

Copyright/Permission Statement

The final publication is available at Springer via http://dx.doi.org/10.1007/s10957-009-9524-5

Comments

At the time of publication, author S. Savin was affiliated with the Columbia University. Currently (July 2016), he is a faculty member in the Operations, Information and Decision Making Department of the Wharton School at the University of Pennsylvania.

Keywords

stochastic control problems with delay, dynamic programming, infinite-dimensional, bellman equations, optimal advertising

 

Date Posted: 27 November 2017

This document has been peer reviewed.