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

Okhrati, Ramin and Schmock, Uwe (2015) Itô's formula for finite variation Lévy processes: the case of non-smooth functions. Journal of Mathematical Analysis and Applications, 430 (2), 1163-1174. (doi:10.1016/j.jmaa.2015.05.025).

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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.

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