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Fast Laplace Transform Methods for Free-Boundary Problems of Fractional Diffusion Equations
Zhou,Zhiqiang1; Ma,Jingtang1; Sun,Hai wei2
2018-01-10
Source PublicationJournal of Scientific Computing
ISSN08857474
Volume74Issue:1Pages:49-69
Abstract

In this paper we develop a fast Laplace transform method for solving a class of free-boundary fractional diffusion equations arising in the American option pricing. Instead of using the time-stepping methods, we develop the Laplace transform methods for solving the free-boundary fractional diffusion equations. By approximating the free boundary, the Laplace transform is taken on a fixed space region to replace discretizing the temporal variable. The hyperbola contour integral method is exploited to restore the option values. Meanwhile, the coefficient matrix has theoretically proven to be sectorial. Therefore, the highly accurate approximation by the fast Laplace transform method is guaranteed. The numerical results confirm that the proposed method outperforms the full finite difference methods in regard to the accuracy and complexity.

KeywordAmerican Option Pricing Fractional Diffusion Equations Free-boundary Problems Hyperbola Contour Integral Laplace Transform Methods Toeplitz Matrix
DOI10.1007/s10915-017-0423-x
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000419601500003
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Cited Times [WOS]:9   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionFaculty of Science and Technology
Personal research not belonging to the institution
Affiliation1.School of Economic MathematicsSouthwestern University of Finance and Economics,Wenjiang, Chengdu,611130,China
2.Department of MathematicsUniversity of Macau,Taipa,Macao
Recommended Citation
GB/T 7714
Zhou,Zhiqiang,Ma,Jingtang,Sun,Hai wei. Fast Laplace Transform Methods for Free-Boundary Problems of Fractional Diffusion Equations[J]. Journal of Scientific Computing,2018,74(1):49-69.
APA Zhou,Zhiqiang,Ma,Jingtang,&Sun,Hai wei.(2018).Fast Laplace Transform Methods for Free-Boundary Problems of Fractional Diffusion Equations.Journal of Scientific Computing,74(1),49-69.
MLA Zhou,Zhiqiang,et al."Fast Laplace Transform Methods for Free-Boundary Problems of Fractional Diffusion Equations".Journal of Scientific Computing 74.1(2018):49-69.
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