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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 83, 2011 - Issue 4-6: Optimal stopping with Applications
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Original Articles

A harmonic function technique for the optimal stopping of diffusions

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Pages 347-363 | Received 29 Oct 2009, Accepted 02 Jun 2010, Published online: 09 Jun 2011
 

Abstract

We consider problems of optimal stopping where the driving process is a (one- or multi-dimensional) diffusion. Our approach is motivated by a change of measure techniques and gives a characterization of the optimal stopping set in terms of harmonic functions for one-dimensional diffusions. The generalization to multidimensional diffusions uses the theory of Martin boundaries. Various applications, including exchange options, are given. We treat an example where halfspaces, which are plausible candidates for the optimal stopping set, are in fact strict subsets of it.

Acknowledgement

We thank the Associated Editor and the referee for their thoughtful and valuable comments.

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