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
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.
|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|
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