A model for optimal stopping in advertisement
type: Item
instance of: scholarly article
title: A model for optimal stopping in advertisement
zbMATH Open document ID: 1208.60040
published in: Nonlinear Analysis. Real World Applications
publication date: 2010-06-03T00:00:00Z
review text: The authors consider the stochastic version of the Bass model described by the following Ito stochastic differential equation \[ dx(t)= [a(1- x(t))+ bx(t)(1- x(t))]\,dt+\sigma a(1- x(t))\,dw(t), \] where \(x\in\mathbb{R}\) is the state variable, \(w(t)\) is the standard Wiener process, \(a\), \(b\), \(\sigma\) are positive constants. The authors studied two problems: the optimal stopping problem and a combined optimal stopping and control problem for the optimization of the advertisement effectiveness. The first problem by reducing it to a free boundary problem was solved numerically by an iterative procedure while the second problem by applying a finite difference scheme. In both problems the obtained results are illustrated by numerical examples.
reviewed by: L. Socha
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 91B70
zbMATH DE Number: 5716697
zbMATH Keywords: optimal stopping problems
zbMATH Keywords: stochastic control
zbMATH Keywords: viscosity solutions
zbMATH Keywords: advertisement diffusion model
author: C. V. Nikolopoulos
author: Athanasios Yannacopoulos
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2009.02.012
OpenAlex ID: W2035960921
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DOI: 10.1016/J.NONRWA.2009.02.012
description: scientific article; zbMATH DE number 5716697