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dc.contributor.authorGlau, K
dc.date.accessioned2017-12-05T11:41:37Z
dc.date.available2017-12-05T11:41:37Z
dc.date.issued2016-10
dc.date.submitted2017-11-30T14:54:51.941Z
dc.identifier.citationGlau, K. (2017). A Feynman–Kac-type formula for Lévy processes with discontinuous killing rates. [online] Finance and Stochastics. Available at: https://link.springer.com/article/10.1007%2Fs00780-016-0301-7 [Accessed 5 Dec. 2017].en_US
dc.identifier.issn0949-2984
dc.identifier.urihttp://qmro.qmul.ac.uk/xmlui/handle/123456789/29091
dc.description.abstractThe challenge to fruitfully merge state-of-the-art techniques from mathematical finance and numerical analysis has inspired researchers to develop fast deterministic option pricing methods. As a result, highly efficient algorithms to compute option prices in Lévy models by solving partial integro-differential equations have been developed. In order to provide a solid mathematical foundation for these methods, we derive a Feynman–Kac representation of variational solutions to partial integro-differential equations that characterize conditional expectations of functionals of killed time-inhomogeneous Lévy processes. We allow a wide range of underlying stochastic processes, comprising processes with Brownian part as well as a broad class of pure jump processes such as generalized hyperbolic, multivariate normal inverse Gaussian, tempered stable, and αα -semistable Lévy processes. By virtue of our mild regularity assumptions as to the killing rate and the initial condition of the partial integro-differential equation, our results provide a rigorous basis for numerous applications in financial mathematics and in probability theory. We implement a Galerkin scheme to solve the corresponding pricing equation numerically and illustrate the effect of a killing rate.en_US
dc.description.sponsorshipThe roots of the present paper go back to the author’s dissertation [17], which was financially supported by the DFG through project EB66/11-1.en_US
dc.format.extent1021 - 1059
dc.publisherSpringeren_US
dc.relation.ispartofFinance and Stochastics
dc.rightsOpen Access: This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
dc.titleA Feynman–Kac-type formula for Lévy processes with discontinuous killing ratesen_US
dc.rights.holder© The Author(s) 2016
dc.identifier.doi10.1007/s00780-016-0301-7
pubs.issue4
pubs.organisational-group/Queen Mary University of London
pubs.organisational-group/Queen Mary University of London/Faculty of Science & Engineering
pubs.organisational-group/Queen Mary University of London/Faculty of Science & Engineering/Mathematical Sciences - Staff and Research Students
pubs.publication-statusPublished
pubs.volume20


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