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Engineering Science and Materials Commons

Open Access. Powered by Scholars. Published by Universities.®

2009

University of Pennsylvania

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Full-Text Articles in Engineering Science and Materials

On Controlled Linear Diffusions With Delay In A Model Of Optimal Advertising Under Uncertainty With Memory Effects, Fausto Gozzi, Carlo Marinelli, Sergei Savin Aug 2009

On Controlled Linear Diffusions With Delay In A Model Of Optimal Advertising Under Uncertainty With Memory Effects, Fausto Gozzi, Carlo Marinelli, Sergei Savin

Operations, Information and Decisions Papers

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 ...