English

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.

Keywords

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

R2 v1 2026-06-23T16:30:06.697Z