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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:430

Article

Okhrati, Ramin¹  Schmock, Uwe² 

[1] Univ Southampton, Southampton, Hants, England

[2] Vienna Univ Technol, A-1040 Vienna, Austria

关键词: Ito's formula;    Finite variation Levy process;    Weak derivative;    PIDE;   

DOI  :  10.1016/j.jmaa.2015.05.025

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free