Simplified calculus for semimartingales: Multiplicative compensators and changes of measure

Ale\v{s} \v{C}ern\'y and Johannes Ruf
Authors registered in the RePEc Author Service: Aleš Černý

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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 L\'evy--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 L\'evy setting.

Date: 2020-06, Revised 2023-05
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Citations: View citations in EconPapers (4)

Published in Stochastic Processes and Their Applications 161, 572-602, 2023

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Journal Article: Simplified calculus for semimartingales: Multiplicative compensators and changes of measure (2023)
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