East Asian J. Appl. Math., 8 (2018), pp. 782-808.
Published online: 2018-10
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Iterative Laplace transform methods for fractional partial differential equations and fractional partial integro-differential equations arising in European option pricing with the Lévy α-stable processes and regime-switching or state-dependent jump rates are studied and numerical contour integral methods to inverse the Laplace transform are developed. It is shown that the methods under consideration have the second-order convergence rate in space and spectral-order convergence for Laplace transform inversion.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.130218.290618}, url = {http://global-sci.org/intro/article_detail/eajam/12819.html} }Iterative Laplace transform methods for fractional partial differential equations and fractional partial integro-differential equations arising in European option pricing with the Lévy α-stable processes and regime-switching or state-dependent jump rates are studied and numerical contour integral methods to inverse the Laplace transform are developed. It is shown that the methods under consideration have the second-order convergence rate in space and spectral-order convergence for Laplace transform inversion.