Abstract.
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 compensator of 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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Manuscript received: January 2001; final version received: November 2001
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Kallsen, J., Shiryaev, A. The cumulant process and Esscher's change of measure. Finance Stochast 6, 397–428 (2002). https://doi.org/10.1007/s007800200069
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DOI: https://doi.org/10.1007/s007800200069