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/j.spa.2023.04.010
Abstract
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 https://creativecommons.org/licenses/by-nc-nd/4.0/ |
| 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 |
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