Gapeev, Pavel V. 
ORCID: 0000-0002-1346-2074 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 |
| Divisions: | Mathematics |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 20 Apr 2012 09:06 |
| Last Modified: | 11 Oct 2025 21:33 |
| URI: | http://eprints.lse.ac.uk/id/eprint/43299 |
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