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Simplified calculus for semimartingales: Multiplicative compensators and changes of measure

Černý, A. ORCID: 0000-0001-5583-6516 & Ruf, J. (2023). Simplified calculus for semimartingales: Multiplicative compensators and changes of measure. Stochastic Processes and their Applications, 161, pp. 572-602. doi: 10.1016/


The paper develops multiplicative compensation for complex-valued semimartingales and studies some of its consequences. It is shown that the stochastic exponential of any complex-valued semimartingale with independent increments becomes a true martingale after multiplicative compensation, where such compensation is meaningful. This generalization of the L\'evy-Khintchin formula fills an existing gap in the literature. We further report Girsanov-type results based on non-negative multiplicatively compensated semimartingales. In particular, we obtain a simplified expression for the multiplicative compensator under the new measure.

Publication Type: Article
Additional Information: © 2023. This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Publisher Keywords: Girsanov, Levy-Khintchin, Mellin transform, Predictable compensator, Process with independent increments, Semimartingale representation
Subjects: H Social Sciences > HG Finance
Departments: Bayes Business School > Finance
[thumbnail of Paper_III_elsart_final.pdf] Text - Accepted Version
This document is not freely accessible until 21 April 2024 due to copyright restrictions.
Available under License Creative Commons Attribution Non-commercial No Derivatives.

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