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The Cumulant Process And Esscher's Change Of Measure

J. Kallsen, A. Shiryaev
Published 2002 · Computer Science, Mathematics

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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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