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Itô's formula for finite variation Lévy processes: The case of non-smooth functions

Okhrati, R; Schmock, U; (2015) Itô's formula for finite variation Lévy processes: The case of non-smooth functions. Journal of Mathematical Analysis and Applications , 430 (2) pp. 1163-1174. 10.1016/j.jmaa.2015.05.025. Green open access

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Abstract

Extending Itô's formula to non-smooth functions is important both in theory and applications. One of the fairly general extensions of the formula, known as Meyer–Itô, applies to one dimensional semimartingales and convex functions. There are also satisfactory generalizations of Itô's formula for diffusion processes where the Meyer–Itô assumptions are weakened even further. We study a version of Itô's formula for multi-dimensional finite variation Lévy processes assuming that the underlying function is continuous and admits weak derivatives. We also discuss some applications of this extension, particularly in finance.

Type: Article
Title: Itô's formula for finite variation Lévy processes: The case of non-smooth functions
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.jmaa.2015.05.025
Publisher version: https://doi.org/10.1016/j.jmaa.2015.05.025
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Itô's formula, Finite variation Lévy process, Weak derivative, PIDE
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Civil, Environ and Geomatic Eng
URI: https://discovery.ucl.ac.uk/id/eprint/10081497
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