Simplified stochastic calculus via semimartingale representations
Probability
2022-01-13 v5 Mathematical Finance
Abstract
We develop a stochastic calculus that makes it easy to capture a variety of predictable transformations of semimartingales such as changes of variables, stochastic integrals, and their compositions. The framework offers a unified treatment of real-valued and complex-valued semimartingales. The proposed calculus is a blueprint for the derivation of new relationships among stochastic processes with specific examples provided below.
Cite
@article{arxiv.2006.11914,
title = {Simplified stochastic calculus via semimartingale representations},
author = {Aleš Černý and Johannes Ruf},
journal= {arXiv preprint arXiv:2006.11914},
year = {2022}
}
Comments
32 pages; updated references; fixed a small typo in proof of T3.17