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L<sup>∞</sup>-Asymptotic Behavior of the Variational Inequality Related to American Options Problem
Department of Mathematics, Faculty of Science, Badji-Mokhtar-Annaba University, P.O. Box 12, Annaba, Algeria
Department of Mathematics, Faculty of Science, Badji-Mokhtar-Annaba University, P.O. Box 12, Annaba, Algeria
- 1 Department of Mathematics, Faculty of Science, Badji-Mokhtar-Annaba University, P.O. Box 12, Annaba, Algeria
- 2 Department of Mathematics, Faculty of Science, Badji-Mokhtar-Annaba University, P.O. Box 12, Annaba, Algeria
Applied Mathematics·Volume 05 (2014)·Pages 1299–1309·Published 24 April 2014·DOI10.4236/am.2014.58122
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Abstract
We study the approximation of variational inequality related to American options problem. A simple proof to asymptotic behavior is also given using the theta time scheme combined with a finite element spatial approximation in uniform norm, which enables us to locate free boundary in practice.
KeywordsAmerican OptionsFinite ElementsParabolic Variational InequalitiesFixed PointAsymptotic Behavior
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