Ito's formula for finite variation Levy processes: The case of non-smooth functions

作者：Okhrati Ramin^*; Schmock Uwe

来源：Journal of Mathematical Analysis and Applications, 2015, 430(2): 1163-1174.

DOI：10.1016/j.jmaa.2015.05.025

• Ito's formula
• Finite variation Levy process
• Weak derivative
• PIDE

Extending Ito'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 Ito, applies to one dimensional semimartingales and convex functions. There are also satisfactory generalizations of Ito's formula for diffusion processes where the Meyer Ito assumptions are weakened even further. We study a version of Ito's formula for multi-dimensional finite variation Levy processes assuming that the underlying function is continuous and admits weak derivatives. We also discuss some applications of this extension, particularly in finance.

• 出版日期2015-10-15