| Title:
|
Superconvergence estimates of finite element methods for American options (English) |
| Author:
|
Lin, Qun |
| Author:
|
Liu, Tang |
| Author:
|
Zhang, Shuhua |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
54 |
| Issue:
|
3 |
| Year:
|
2009 |
| Pages:
|
181-202 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. {\it 39} (2001), 834--857, 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 $L^2$-, $L^{\infty }$-norm error estimates and an $H^1$-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. (English) |
| Keyword:
|
American options |
| Keyword:
|
variational inequality |
| Keyword:
|
finite element methods |
| Keyword:
|
optimal and superconvergent estimates |
| Keyword:
|
interpolation postprocessing |
| Keyword:
|
a posteriori error estimators |
| MSC:
|
65K10 |
| MSC:
|
65K15 |
| MSC:
|
65M12 |
| MSC:
|
65M60 |
| MSC:
|
90A09 |
| MSC:
|
91G10 |
| MSC:
|
91G20 |
| MSC:
|
91G60 |
| idZBL:
|
Zbl 1212.65252 |
| idMR:
|
MR2530538 |
| DOI:
|
10.1007/s10492-009-0012-x |
| . |
| Date available:
|
2010-07-20T12:56:28Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140359 |
| . |
| Reference:
|
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| . |
