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

Text - Accepted Version This document is not freely accessible due to copyright restrictions. Available under License Creative Commons Attribution Non-commercial No Derivatives. To request a copy, please use the button below. Request a copy

Export

Downloads