The damped Crank-Nicolson time-marching scheme for the adaptive solution of the Black-Scholes equation
This paper is concerned with the derivation of a residual-based a posteriori error estimator and mesh-adaptation strategies for the space-time finite element approximation of parabolic problems with irregular data. Typical applications arise in the field of mathematical finance, where the Black-Scho...
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| Hauptverfasser: | , , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
30 April 2015
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| In: |
The journal of computational finance
Year: 2015, Jahrgang: 18, Heft: 4, Pages: 1-37 |
| ISSN: | 1755-2850 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://www.risk.net/journal-of-computational-finance/2406534/the-damped-crank-nicolson-time-marching-scheme-for-the-adaptive-solution-of-the-black-scholes-equation
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| Verfasserangaben: | Christian Goll, Rolf Rannacher and Winnifried Wollner |
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| 520 | |a This paper is concerned with the derivation of a residual-based a posteriori error estimator and mesh-adaptation strategies for the space-time finite element approximation of parabolic problems with irregular data. Typical applications arise in the field of mathematical finance, where the Black-Scholes equation is used for modeling the pricing of European options. A conforming finite element discretization in space is combined with second-order time discretization by a damped Crank-Nicolson scheme for coping with data irregularities in the model. The a posteriori error analysis is developed within the general framework of the dual weighted residual method for sensitivity-based, goal-oriented error estimation and mesh optimization. In particular, the correct form of the dual problem with damping is considered. | ||
| 650 | 4 | |a Black-Scholes equation | |
| 650 | 4 | |a space-time finite elements | |
| 650 | 4 | |a damped Crank-Nicolson method | |
| 650 | 4 | |a goal-oriented adaptivity | |
| 650 | 4 | |a DWR method | |
| 650 | 4 | |a adjoint consistent | |
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