Journal
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES
Volume 83, Issue 4-6, Pages 347-363Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/17442508.2010.498915
Keywords
optimal stopping; diffusions; harmonic functions; Martin boundary; exchange options
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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.
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