Bounds for a constrained optimal stopping problem |
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Authors: | Cloud Makasu |
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Affiliation: | (1) Department of Mathematics and Applied Mathematics, University of Venda, Private Bag X5050, Thohoyandou, 0950, South Africa |
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Abstract: | In this short letter, we present an explicit upper bound for the optimal value of a bidimensional optimal stopping problem over stopping times τ subject to a constraint , where x(.) is a geometric Brownian motion coupled with an arbitrary diffusion process y(.), θ(., .) and c(.) are given positive, continuous functions and β > 0 is a fixed constant. The present result is derived from a corresponding Lagrangian dual problem, and using a recent result of Makasu (Seq Anal 27:435–440, 2008). Examples are given to illustrate our main result. Partial results of this note were obtained when the author was holding a postdoc grant PRO12/1003 at the Mathematics Institute, University of Oslo, Norway. |
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Keywords: | Constrained optimal stopping problem Lagrangian dual problem Lagrangian multiplier |
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