Gapeev, Pavel V. and Lerche, Hans Rudolf (2011) On the structure of discounted optimal stopping problems for one-dimensional diffusions. Stochastics: an international journal of probability and stochastic processes, 83 (4-6). pp. 537-554. ISSN 1744-2508
Abstract
We connect two approaches for solving discounted optimal stopping problems for one-dimensional time-homogeneous regular diffusion processes on infinite time intervals. The optimal stopping rule is assumed to be the first exit time of the underlying process from a region restricted by two constant boundaries. We provide an explicit decomposition of the reward process into a product of a gain function of the boundaries and a uniformly integrable martingale inside the continuation region. This martingale plays a key role for stating sufficient conditions for the optimality of the first exit time. We also consider several illustrating examples of rational valuation of perpetual American strangle options. © 2011 Copyright Taylor and Francis Group, LLC.
| Item Type: | Article |
|---|---|
| Official URL: | http://dx.doi.org/10.1080/17442508.2010.532874 |
| Additional Information: | © 2011 Copyright Taylor & Francis |
| Uncontrolled Keywords: | ISI, diffusion process, first exit time, free-boundary problem, martingale approach of Beibel and Lerche, optimal stopping problem, perpetual American strangle options |
| Library of Congress subject classification: | Q Science > QA Mathematics |
| Sets: | Departments > Mathematics |
| Rights: | http://www.lse.ac.uk/library/rights/LSERO.htm |
| URL: | http://eprints.lse.ac.uk/43299/ |
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