The cumulant process and Esscher's change of measure

@article{Kallsen2002TheCP,
  title={The cumulant process and Esscher's change of measure},
  author={Jan Kallsen and Albert N. Shiryaev},
  journal={Finance and Stochastics},
  year={2002},
  volume={6},
  pages={397-428}
}
In this paper two kinds of cumulant processes are studied in a general setting. These processes generalize the cumulant of an infinitely divisible random variable and they appear as the exponential compensatorf a semimartingale. In a financial context cumulant processes lead to a generalized Esscher transform. We also provide some new criteria for uniform integrability of exponential martingales. 
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