Functional Meyer-Tanaka Formula
Probability
2018-06-19 v4
Abstract
The functional Ito formula, firstly introduced by Bruno Dupire for continuous semimartingales, might be extended in two directions: different dynamics for the underlying process and/or weaker assumptions on the regularity of the functional. In this paper, we pursue the former type by proving the functional version of the Meyer-Tanaka Formula. Following the idea of the proof of the classical time-dependent Meyer-Tanaka formula, we study the mollification of functionals and its convergence properties. As an example, we study the running maximum and the max-martingales of Yor and Obloj.
Cite
@article{arxiv.1408.4193,
title = {Functional Meyer-Tanaka Formula},
author = {Yuri F. Saporito},
journal= {arXiv preprint arXiv:1408.4193},
year = {2018}
}
Comments
26 pages, 2 figures