Simplified Stochastic Calculus via Semimartingale Representations

arXiv preprint 2006.11914

27 Pages Posted: 23 Jun 2020 Last revised: 25 Sep 2020

See all articles by Aleš Černý

Aleš Černý

The Business School (formerly Cass), City, University of London

Johannes Ruf

London School of Economics & Political Science (LSE) - London School of Economics

Date Written: June 21, 2020

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 in the paper.

Keywords: Complex-valued process; generalized Yor formula; Émery formula; Itô formula

JEL Classification: C65, G11

Suggested Citation

Černý, Aleš and Ruf, Johannes, Simplified Stochastic Calculus via Semimartingale Representations (June 21, 2020). arXiv preprint 2006.11914, Available at SSRN: https://ssrn.com/abstract=3633638 or http://dx.doi.org/10.2139/ssrn.3633638

Aleš Černý (Contact Author)

The Business School (formerly Cass), City, University of London ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Johannes Ruf

London School of Economics & Political Science (LSE) - London School of Economics ( email )

United Kingdom

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