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Simplified calculus for semimartingales: multiplicative compensators and changes of measure

Černý, Aleš and Ruf, Johannes ORCID: 0000-0003-3616-2194 (2023) Simplified calculus for semimartingales: multiplicative compensators and changes of measure. Stochastic Processes and Their Applications, 161. pp. 572-602. ISSN 0304-4149

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Identification Number: 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 when such compensation is meaningful. This generalization of the Lévy–Khintchin formula fills an existing gap in the literature. It allows, for example, the computation of the Mellin transform of a signed stochastic exponential, which in turn has practical applications in mean–variance portfolio theory. Girsanov-type results based on multiplicatively compensated semimartingales simplify treatment of absolutely continuous measure changes. As an example, we obtain the characteristic function of log returns for a popular class of minimax measures in a Lévy setting.

Item Type: Article
Additional Information: © 2023 Elsevier.
Divisions: Mathematics
Date Deposited: 13 Apr 2023 09:36
Last Modified: 19 May 2024 06:24
URI: http://eprints.lse.ac.uk/id/eprint/118618

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