Stochastic Optimal Control of Delay Equations Arising in Advertising Models

نویسندگان

  • Fausto Gozzi
  • Carlo Marinelli
چکیده

We consider a class of optimal control problems of stochastic delay differential equations (SDDE) that arise in connection with optimal advertising under uncertainty for the introduction of a new product to the market, generalizing classical work of Nerlove and Arrow [30]. In particular, we deal with controlled SDDE where the delay enters both the state and the control. Following ideas of Vinter and Kwong [34] (which however hold only in the deterministic case), we reformulate the problem as an infinite dimensional stochastic control problem to which we associate, through the dynamic programming principle, a second order Hamilton-Jacobi-Bellman equation. We show a verification theorem and we exhibit some simple cases where such equation admits an explicit smooth solution, allowing us to construct optimal feedback controls.

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تاریخ انتشار 2005