Download This PaperSimplified Stochastic Calculus via Semimartingale Representations
Electronic Journal of Probability, 2022, 27, paper no.3, 1-32
32 Pages Posted: 23 Jun 2020 Last revised: 19 Apr 2022
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
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