Simplified calculus for semimartingales: Multiplicative compensators and changes of measure

The paper develops multiplicative compensation for complex-valued semimartingales and studies some of its consequences. It is shown that the stochastic exponential any semimartingale with independent increments becomes a true martingale after when such meaningful. This generalization L\'evy--Khintchin formula fills an existing gap in literature. allows, example, computation Mellin transform signed exponential, which turn has practical applications mean--variance portfolio theory. Girsanov-type results based on multiplicatively compensated simplify treatment absolutely continuous measure changes. As we obtain characteristic function log returns popular class minimax measures L\'evy setting.