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Superconvergence estimates of finite element methods for American options.
- Source :
-
Applications of Mathematics . Jun2009, Vol. 54 Issue 3, p181-202. 22p. - Publication Year :
- 2009
-
Abstract
- In this paper we are concerned with finite element approximations to the evaluation of American options. First, following W. Allegretto etc., SIAM J. Numer. Anal. 39 (2001), 834ā857, we introduce a novel practical approach to the discussed problem, which involves the exact reformulation of the original problem and the implementation of the numerical solution over a very small region so that this algorithm is very rapid and highly accurate. Secondly by means of a superapproximation and interpolation postprocessing analysis technique, we present sharp L2-, Lā-norm error estimates and an H1-norm superconvergence estimate for this finite element method. As a by-product, the global superconvergence result can be used to generate an efficient a posteriori error estimator. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 08627940
- Volume :
- 54
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Applications of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 41429359
- Full Text :
- https://doi.org/10.1007/s10492-009-0012-x