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The cumulant process and Esscher's change of measure

Albert N. Shiryaev () and Jan Kallsen ()
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Albert N. Shiryaev: Steklov Mathematical Institute, Gubkina St. 8, 117966 Moscow, Russia Manuscript
Jan Kallsen: Institut für Mathematische Stochastik, Universität Freiburg, Eckerstraße 1, 79104 Freiburg i. Br., Germany

Finance and Stochastics, 2002, vol. 6, issue 4, 397-428

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.

Keywords: Cumulant process; stochastic logarithm; exponential transform; exponential compensator; exponentially special semimartingale; Esscher transform; uniform integrability (search for similar items in EconPapers)
JEL-codes: G13 D52 (search for similar items in EconPapers)
Date: 2002-08-19
Note: received: January 2001; final version received: November 2001
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